def _test_distance_correlation_vector_generic(self,
vector_type=None,
type_cov=None,
type_cor=None):
"""
Auxiliar function for testing distance correlation in vectors.
This function is provided to check that the results are the
same with different dtypes, but that the dtype of the result is
the right one.
"""
if type_cov is None:
type_cov = vector_type
if type_cor is None:
type_cor = vector_type
arr1 = np.array([
vector_type(1),
vector_type(2),
vector_type(3),
vector_type(4),
vector_type(5),
vector_type(6)
])
arr2 = np.array([
vector_type(1),
vector_type(7),
vector_type(5),
vector_type(5),
vector_type(6),
vector_type(2)
])
covariance = dcor.distance_covariance_sqr(arr1, arr2)
self.assertIsInstance(covariance, type_cov)
self.assertAlmostEqual(covariance, type_cov(0.6851851), places=6)
correlation = dcor.distance_correlation_sqr(arr1, arr2)
self.assertIsInstance(correlation, type_cor)
self.assertAlmostEqual(correlation, type_cor(0.3066099), places=6)
print(covariance, correlation)
covariance = dcor.distance_covariance_sqr(arr1, arr1)
self.assertIsInstance(covariance, type_cov)
self.assertAlmostEqual(covariance, type_cov(1.706791), places=5)
correlation = dcor.distance_correlation_sqr(arr1, arr1)
self.assertIsInstance(correlation, type_cor)
self.assertAlmostEqual(correlation, type_cor(1), places=5)
print(covariance, correlation)
def test_distance_correlation_naive(self):
"""Compare distance correlation with the energy package."""
matrix1 = np.array(((1, 2, 3), (4, 5, 6), (7, 8, 9)))
matrix2 = np.array(((7, 3, 6), (2, 1, 4), (3, 8, 1)))
matrix3 = np.array(((1, 1, 1), (2, 1, 1), (1, 1, 1)))
constant_matrix = np.ones((3, 3))
correlation = dcor.distance_correlation_sqr(matrix1, matrix1)
self.assertAlmostEqual(correlation, 1)
correlation = dcor.distance_correlation_sqr(matrix1, constant_matrix)
self.assertAlmostEqual(correlation, 0)
correlation = dcor.distance_correlation_sqr(matrix1, matrix2)
self.assertAlmostEqual(correlation, 0.93387, places=5)
correlation = dcor.distance_correlation_sqr(matrix1, matrix3)
self.assertAlmostEqual(correlation, 0.31623, places=5)
def test_statistic(self):
"""Test that the fast and naive algorithms for biased dcor match"""
for seed in range(5):
random_state = np.random.RandomState(seed)
for i in range(4, self.test_max_size + 1):
arr1 = random_state.rand(i, 1)
arr2 = random_state.rand(i, 1)
stat = dcor.distance_correlation_sqr(
arr1, arr2, method='naive')
for method in dcor.DistanceCovarianceMethod:
with self.subTest(method=method):
stat2 = dcor.distance_correlation_sqr(
arr1, arr2, method=method)
self.assertAlmostEqual(stat, stat2)
def test_distance_correlation_comparison(self):
"""
Compare all implementations of the distance covariance and correlation.
"""
arr1 = np.array(((1.,), (2.,), (3.,), (4.,), (5.,), (6.,)))
arr2 = np.array(((1.,), (7.,), (5.,), (5.,), (6.,), (2.,)))
for method in dcor.DistanceCovarianceMethod:
with self.subTest(method=method):
compile_modes = [dcor.CompileMode.AUTO,
dcor.CompileMode.COMPILE_CPU,
dcor.CompileMode.NO_COMPILE]
if method is not dcor.DistanceCovarianceMethod.NAIVE:
compile_modes += [dcor.CompileMode.COMPILE_CPU]
for compile_mode in compile_modes:
with self.subTest(compile_mode=compile_mode):
# Unbiased versions
covariance = dcor.u_distance_covariance_sqr(
arr1, arr2, method=method,
compile_mode=compile_mode)
self.assertAlmostEqual(covariance, -0.88889, places=5)
correlation = dcor.u_distance_correlation_sqr(
arr1, arr2, method=method,
compile_mode=compile_mode)
self.assertAlmostEqual(correlation, -0.41613, places=5)
covariance = dcor.u_distance_covariance_sqr(
arr1, arr1, method=method,
compile_mode=compile_mode)
self.assertAlmostEqual(covariance, 1.55556, places=5)
correlation = dcor.u_distance_correlation_sqr(
arr1, arr1, method=method,
compile_mode=compile_mode)
self.assertAlmostEqual(correlation, 1, places=5)
covariance = dcor.u_distance_covariance_sqr(
arr2, arr2, method=method,
compile_mode=compile_mode)
self.assertAlmostEqual(covariance, 2.93333, places=5)
correlation = dcor.u_distance_correlation_sqr(
arr2, arr2, method=method,
compile_mode=compile_mode)
self.assertAlmostEqual(correlation, 1, places=5)
stats = dcor.u_distance_stats_sqr(
arr1, arr2, method=method,
compile_mode=compile_mode)
np.testing.assert_allclose(
stats, (-0.88889, -0.41613, 1.55556, 2.93333),
rtol=1e-4)
# Biased
covariance = dcor.distance_covariance_sqr(
arr1, arr2, method=method,
compile_mode=compile_mode)
self.assertAlmostEqual(covariance, 0.68519, places=5)
correlation = dcor.distance_correlation_sqr(
arr1, arr2, method=method,
compile_mode=compile_mode)
self.assertAlmostEqual(correlation, 0.30661, places=5)
covariance = dcor.distance_covariance_sqr(
arr1, arr1, method=method,
compile_mode=compile_mode)
self.assertAlmostEqual(covariance, 1.70679, places=5)
correlation = dcor.distance_correlation_sqr(
arr1, arr1, method=method,
compile_mode=compile_mode)
self.assertAlmostEqual(correlation, 1, places=5)
covariance = dcor.distance_covariance_sqr(
arr2, arr2, method=method,
compile_mode=compile_mode)
self.assertAlmostEqual(covariance, 2.92593, places=5)
correlation = dcor.distance_correlation_sqr(
arr2, arr2, method=method,
compile_mode=compile_mode)
self.assertAlmostEqual(correlation, 1, places=5)
stats = dcor.distance_stats_sqr(
arr1, arr2, method=method,
compile_mode=compile_mode)
np.testing.assert_allclose(
stats, (0.68519, 0.30661, 1.70679, 2.92593),
rtol=1e-4)