# distance_covariance_sqr#

distance_covariance_sqr(x, y, *, exponent=1, method=DistanceCovarianceMethod.AUTO, compile_mode=CompileMode.AUTO)[source]#

Usual (biased) estimator for the squared distance covariance.

Parameters
• x (Array) – First random vector. The columns correspond with the individual random variables while the rows are individual instances of the random vector.

• y (Array) – Second random vector. The columns correspond with the individual random variables while the rows are individual instances of the random vector.

• exponent (float) – Exponent of the Euclidean distance, in the range $$(0, 2)$$. Equivalently, it is twice the Hurst parameter of fractional Brownian motion.

• method (Union[DistanceCovarianceMethod, Literal['auto', 'naive', 'avl', 'mergesort']]) – Method to use internally to compute the distance covariance.

• compile_mode (CompileMode) – Compilation mode used. By default it tries to use the fastest available type of compilation.

Returns

Biased estimator of the squared distance covariance.

Return type

Array

distance_covariance u_distance_covariance_sqr

Examples

>>> import numpy as np
>>> import dcor
>>> a = np.array([[1., 2., 3., 4.],
...               [5., 6., 7., 8.],
...               [9., 10., 11., 12.],
...               [13., 14., 15., 16.]])
>>> b = np.array([[1.], [0.], [0.], [1.]])
>>> dcor.distance_covariance_sqr(a, a)
52.0
>>> dcor.distance_covariance_sqr(a, b)
1.0
>>> dcor.distance_covariance_sqr(b, b)
0.25
>>> dcor.distance_covariance_sqr(a, b, exponent=0.5)
0.3705904...


## Examples using dcor.distance_covariance_sqr#

Performance of the methods

Performance of the methods