def test_quadtree_similar_point():
# Introduce a point into a quad tree where a similar point already exists.
# Test will hang if it doesn't complete.
Xs = []
# check the case where points are actually different
Xs.append(np.array([[1, 2], [3, 4]], dtype=np.float32))
# check the case where points are the same on X axis
Xs.append(np.array([[1.0, 2.0], [1.0, 3.0]], dtype=np.float32))
# check the case where points are arbitrarily close on X axis
Xs.append(np.array([[1.00001, 2.0], [1.00002, 3.0]], dtype=np.float32))
# check the case where points are the same on Y axis
Xs.append(np.array([[1.0, 2.0], [3.0, 2.0]], dtype=np.float32))
# check the case where points are arbitrarily close on Y axis
Xs.append(np.array([[1.0, 2.00001], [3.0, 2.00002]], dtype=np.float32))
# check the case where points are arbitrarily close on both axes
Xs.append(
np.array([[1.00001, 2.00001], [1.00002, 2.00002]], dtype=np.float32))
# check the case where points are arbitrarily close on both axes
# close to machine epsilon - x axis
Xs.append(
np.array([[1, 0.0003817754041], [2, 0.0003817753750]],
dtype=np.float32))
# check the case where points are arbitrarily close on both axes
# close to machine epsilon - y axis
Xs.append(
np.array([[0.0003817754041, 1.0], [0.0003817753750, 2.0]],
dtype=np.float32))
for X in Xs:
tree = _QuadTree(n_dimensions=2, verbose=0)
tree.build_tree(X)
tree._check_coherence()
def test_quad_tree_pickle(n_dimensions, protocol):
rng = check_random_state(0)
X = rng.random_sample((10, n_dimensions))
tree = _QuadTree(n_dimensions=n_dimensions, verbose=0)
tree.build_tree(X)
s = pickle.dumps(tree, protocol=protocol)
bt2 = pickle.loads(s)
for x in X:
cell_x_tree = tree.get_cell(x)
cell_x_bt2 = bt2.get_cell(x)
assert cell_x_tree == cell_x_bt2
def test_qt_insert_duplicate(n_dimensions):
rng = check_random_state(0)
X = rng.random_sample((10, n_dimensions))
Xd = np.r_[X, X[:5]]
tree = _QuadTree(n_dimensions=n_dimensions, verbose=0)
tree.build_tree(Xd)
cumulative_size = tree.cumulative_size
leafs = tree.leafs
# Assert that the first 5 are indeed duplicated and that the next
# ones are single point leaf
for i, x in enumerate(X):
cell_id = tree.get_cell(x)
assert leafs[cell_id]
assert cumulative_size[cell_id] == 1 + (i < 5)
def test_quadtree_boundary_computation():
# Introduce a point into a quad tree with boundaries not easy to compute.
Xs = []
# check a random case
Xs.append(np.array([[-1, 1], [-4, -1]], dtype=np.float32))
# check the case where only 0 are inserted
Xs.append(np.array([[0, 0], [0, 0]], dtype=np.float32))
# check the case where only negative are inserted
Xs.append(np.array([[-1, -2], [-4, 0]], dtype=np.float32))
# check the case where only small numbers are inserted
Xs.append(np.array([[-1e-6, 1e-6], [-4e-6, -1e-6]], dtype=np.float32))
for X in Xs:
tree = _QuadTree(n_dimensions=2, verbose=0)
tree.build_tree(X)
tree._check_coherence()
def test_summarize():
# Simple check for quad tree's summarize
angle = 0.9
X = np.array(
[[-10.0, -10.0], [9.0, 10.0], [10.0, 9.0], [10.0, 10.0]], dtype=np.float32
)
query_pt = X[0, :]
n_dimensions = X.shape[1]
offset = n_dimensions + 2
qt = _QuadTree(n_dimensions, verbose=0)
qt.build_tree(X)
idx, summary = qt._py_summarize(query_pt, X, angle)
node_dist = summary[n_dimensions]
node_size = summary[n_dimensions + 1]
# Summary should contain only 1 node with size 3 and distance to
# X[1:] barycenter
barycenter = X[1:].mean(axis=0)
ds2c = ((X[0] - barycenter) ** 2).sum()
assert idx == offset
assert node_size == 3, "summary size = {}".format(node_size)
assert np.isclose(node_dist, ds2c)
# Summary should contain all 3 node with size 1 and distance to
# each point in X[1:] for ``angle=0``
idx, summary = qt._py_summarize(query_pt, X, 0.0)
barycenter = X[1:].mean(axis=0)
ds2c = ((X[0] - barycenter) ** 2).sum()
assert idx == 3 * (offset)
for i in range(3):
node_dist = summary[i * offset + n_dimensions]
node_size = summary[i * offset + n_dimensions + 1]
ds2c = ((X[0] - X[i + 1]) ** 2).sum()
assert node_size == 1, "summary size = {}".format(node_size)
assert np.isclose(node_dist, ds2c)