""" Distance Correlation
Notes
-----
Snippet adapted from: https://gist.github.com/Satra/aa3d19a12b74e9ab7941
"""
# Author: Avraam Marimpis <avraam.marimpis@gmail.com>
import numpy as np
from scipy.spatial.distance import pdist, squareform # type: ignore
[docs]def dcorr(x: np.ndarray, y: np.ndarray) -> float:
""" Distance Correlation
Parameters
----------
x : array-like, shape(n_samples)
Input time series.
y : array-like, shape(N)
Input time series.
Returns
-------
val : float
The computed distance correlation.
"""
lx = len(x)
ly = len(y)
if lx != ly:
raise Exception("")
X = np.atleast_1d(x) # type: ignore
Y = np.atleast_1d(y) # type: ignore
if np.prod(X.shape) == len(X):
X = X[:, None]
if np.prod(Y.shape) == len(Y):
Y = Y[:, None]
X = np.atleast_2d(X)
Y = np.atleast_2d(Y)
n = X.shape[0]
a = squareform(pdist(X))
b = squareform(pdist(Y))
A = a - a.mean(axis=0)[None, :] - a.mean(axis=1)[:, None] + a.mean()
B = b - b.mean(axis=0)[None, :] - b.mean(axis=1)[:, None] + b.mean()
dcov2_xy = (A * B).sum() / float(n * n)
dcov2_xx = (A * A).sum() / float(n * n)
dcov2_yy = (B * B).sum() / float(n * n)
dcor = np.sqrt(dcov2_xy) / np.sqrt(np.sqrt(dcov2_xx) * np.sqrt(dcov2_yy))
return dcor