def test_lp_error_grid_points(self):
grid_points = [1, 2, 4, 4.3, 5]
fd2 = FDataGrid([[2, 3, 4, 5, 6], [1, 4, 9, 16, 25]],
grid_points=grid_points)
with np.testing.assert_raises(ValueError):
lp_distance(self.fd, fd2)
def test_lp_error_domain_ranges(self):
sample_points = [2, 3, 4, 5, 6]
fd2 = FDataGrid([[2, 3, 4, 5, 6], [1, 4, 9, 16, 25]],
sample_points=sample_points)
with np.testing.assert_raises(ValueError):
lp_distance(self.fd, fd2)
def test_lp_grid_basis(self):
np.testing.assert_allclose(lp_distance(self.fd, self.fd_basis), 0)
np.testing.assert_allclose(lp_distance(self.fd_basis, self.fd), 0)
np.testing.assert_allclose(
lp_distance(self.fd_basis,
self.fd_basis,
eval_points=[1, 2, 3, 4, 5]), 0)
np.testing.assert_allclose(lp_distance(self.fd_basis, self.fd_basis),
0)
def test_kneighbors(self):
"""Test k neighbor searches for all k-neighbors estimators"""
nn = NearestNeighbors()
nn.fit(self.X)
lof = LocalOutlierFactor(n_neighbors=5)
lof.fit(self.X)
knn = KNeighborsClassifier()
knn.fit(self.X, self.y)
knnr = KNeighborsRegressor()
knnr.fit(self.X, self.modes_location)
for neigh in [nn, knn, knnr, lof]:
dist, links = neigh.kneighbors(self.X[:4])
np.testing.assert_array_equal(links, [[0, 7, 21, 23, 15],
[1, 12, 19, 18, 17],
[2, 17, 22, 27, 26],
[3, 4, 9, 5, 25]])
graph = neigh.kneighbors_graph(self.X[:4])
dist_kneigh = lp_distance(self.X[0], self.X[7])
np.testing.assert_array_almost_equal(dist[0, 1], dist_kneigh)
for i in range(30):
self.assertEqual(graph[0, i] == 1.0, i in links[0])
self.assertEqual(graph[0, i] == 0.0, i not in links[0])
def test_radius_neighbors(self):
"""Test query with radius"""
nn = NearestNeighbors(radius=.1)
nn.fit(self.X)
knn = RadiusNeighborsClassifier(radius=.1)
knn.fit(self.X, self.y)
knnr = RadiusNeighborsRegressor(radius=.1)
knnr.fit(self.X, self.modes_location)
for neigh in [nn, knn, knnr]:
dist, links = neigh.radius_neighbors(self.X[:4])
np.testing.assert_array_equal(links[0], np.array([0, 7]))
np.testing.assert_array_equal(links[1], np.array([1]))
np.testing.assert_array_equal(links[2], np.array([2, 17, 22, 27]))
np.testing.assert_array_equal(links[3], np.array([3, 4, 9]))
dist_kneigh = lp_distance(self.X[0], self.X[7])
np.testing.assert_array_almost_equal(dist[0][1], dist_kneigh)
graph = neigh.radius_neighbors_graph(self.X[:4])
for i in range(30):
self.assertEqual(graph[0, i] == 1.0, i in links[0])
self.assertEqual(graph[0, i] == 0.0, i not in links[0])
def test_lp_error_dimensions(self):
# Case internal arrays
with np.testing.assert_raises(ValueError):
lp_distance(self.fd, self.fd_surface)
with np.testing.assert_raises(ValueError):
lp_distance(self.fd, self.fd_curve)
with np.testing.assert_raises(ValueError):
lp_distance(self.fd_surface, self.fd_curve)
def v_sample_stat(fd, weights, p=2):
r"""
Calculates a statistic that measures the variability between groups of
samples in a :class:`skfda.representation.FData` object.
The statistic defined as below is calculated between all the samples in a
:class:`skfda.representation.FData` object with a given set of
weights.
Let :math:`\{f_i\}_{i=1}^k` be a set of samples in a FData object.
Let :math:`\{w_j\}_{j=1}^k` be a set of weights, where :math:`w_i` is
related to the sample :math:`f_i` for :math:`i=1,\dots,k`.
The statistic is defined as:
.. math::
V_n = \sum_{i<j}^kw_i\|f_i-f_j\|^2
This statistic is defined in Cuevas[1].
Args:
fd (FData): Object containing all the samples for which we want
to calculate the statistic.
weights (list of int): Weights related to each sample. Each
weight is expected to appear in the same position as its
corresponding sample in the FData object.
p (int, optional): p of the lp norm. Must be greater or equal
than 1. If p='inf' or p=np.inf it is used the L infinity metric.
Defaults to 2.
Returns:
The value of the statistic.
Raises:
ValueError
Examples:
>>> from skfda.inference.anova import v_sample_stat
>>> from skfda.representation.grid import FDataGrid
>>> import numpy as np
We create different trajectories to be applied in the statistic and a
set of weights.
>>> t = np.linspace(0, 1, 50)
>>> x1 = t * (1 - t) ** 5
>>> x2 = t ** 2 * (1 - t) ** 4
>>> x3 = t ** 3 * (1 - t) ** 3
>>> fd = FDataGrid([x1, x2, x3], sample_points=t)
>>> weights = [10, 20, 30]
Finally the value of the statistic is calculated:
>>> v_sample_stat(fd, weights)
0.01649448843348894
References:
[1] Antonio Cuevas, Manuel Febrero-Bande, and Ricardo Fraiman. "An
anova test for functional data". *Computational Statistics Data
Analysis*, 47:111-112, 02 2004
"""
weights = np.asarray(weights)
if not isinstance(fd, FData):
raise ValueError("Argument type must inherit FData.")
if len(weights) != fd.n_samples:
raise ValueError("Number of weights must match number of samples.")
t_ind = np.tril_indices(fd.n_samples, -1)
coef = weights[t_ind[1]]
return np.sum(coef * lp_distance(fd[t_ind[0]], fd[t_ind[1]], p=p) ** p)