Comparison with R’s ‘energy’#

The ‘energy’ package for R provides an implementation of the E-statistics in this package programmed by the original authors of these statistics.

This package is inspired by ‘energy’, and tries to bring the same functionality to a Python audience.

In this section, both packages are compared, to give an overview of the differences, and to make porting code between R and Python easier.

Table of energy-dcor equivalents#

energy (R)

dcor (Python)

Notes

 
dx <- dist(x)
DX <- as.matrix(dx)

DX = dcor.distances.pairwise_distances(x)

Not really part of ‘energy’, but the ‘stats’ package.

In Python it returns a numpy array, while in R it returns a matrix object

 
D_center(DX)

dcor.double_centered(DX)

U_center(DX)

dcor.u_centered(DX)



dcor.mean_product(U, V)

Provided for symmetry with dcor.u_product, although the implementation is very simple

 
U_product(U, V)

dcor.u_product(U, V)



dcor.u_projection(U)



dcor.u_complementary_projection(U)

dcov(x, y)

dcor.distance_covariance(x, y)

In ‘energy’, the distance matrix can be computed beforehand. That is not currently possible in ‘dcor’

 
dcov(x, y, index = 0.5)

dcor.distance_covariance(
    x,
    y,
    exponent = 0.5,
)

In ‘energy’, the distance matrix can be computed beforehand. That is not currently possible in ‘dcor’

 
dcor(x, y)

dcor.distance_correlation(x, y)

In ‘energy’, the distance matrix can be computed beforehand. That is not currently possible in ‘dcor’

 
dcor(x, y, index = 0.5)

dcor.distance_correlation(
    x,
    y,
    exponent = 0.5,
)

In ‘energy’, the distance matrix can be computed beforehand. That is not currently possible in ‘dcor’

 
DCOR(x, y)

dcor.distance_stats(x, y)

In ‘energy’, the distance matrix can be computed beforehand. That is not currently possible in ‘dcor’

 
DCOR(x, y, index = 0.5)

dcor.distance_stats(
    x,
    y,
    exponent = 0.5,
)

In ‘energy’, the distance matrix can be computed beforehand. That is not currently possible in ‘dcor’

 
dcovU(x, y)

dcor.u_distance_covariance_sqr(x, y)

In ‘energy’, the distance matrix can be computed beforehand. That is not currently possible in ‘dcor’

 


dcor.u_distance_covariance_sqr(
    x,
    y,
    exponent = 0.5,
)

bcdcor(x, y)

dcor.u_distance_correlation_sqr(x, y)

In ‘energy’, the distance matrix can be computed beforehand. That is not currently possible in ‘dcor’

 


dcor.u_distance_correlation_sqr(
    x,
    y,
    exponent = 0.5,
)

dx <- dist(x)
dy <- dist(y)

DX <- as.matrix(dx)
DY <- as.matrix(dy)

dcovU_stats(DX, DY)

dcor.u_distance_stats_sqr(x, y)



dcor.u_distance_stats_sqr(
    x,
    y,
    exponent = 0.5,
)



dcor.distance_correlation_af_inv(x, y)

pdcov(x, y, z)

dcor.partial_distance_covariance(x, y, z)

In ‘energy’, the distance matrix can be computed beforehand. That is not currently possible in ‘dcor’

 
pdcor(x, y, z)

dcor.partial_distance_correlation(x, y, z)

In ‘energy’, the distance matrix can be computed beforehand. That is not currently possible in ‘dcor’

 
edist(
    rbind(x, y),
    c(nrow(x), nrow(y))
)

dcor.homogeneity.energy_test_statistic(
    x,
    y,
)

In spite of its name, ‘energy’ function ‘edist’ is not the energy distance, but a test statistic.

The ‘energy’ version computes all pairwise estimations between clusters. The ‘dcor’ version computes only the statistic between two random variables.

The only method supported in ‘dcor’ is ‘cluster’.

 
edist(
    rbind(x, y),
    c(nrow(x), nrow(y)),
    alpha = 0.5,
    method="cluster"
)

dcor.homogeneity.energy_test_statistic(
    x,
    y,
    exponent=0.5,
)

In spite of its name, ‘energy’ function ‘edist’ is not the energy distance, but a test statistic.

The ‘energy’ version computes all pairwise estimations between clusters. The ‘dcor’ version computes only the statistic between two random variables.

The only method supported in ‘dcor’ is ‘cluster’.

 


dcor.energy_distance(x, y)

eqdist.etest(
    rbind(x, y, z),
    c(nrow(x), nrow(y), nrow(z)),
    R=10
)

dcor.homogeneity.energy_test(
    x,
    y,
    z,
    num_resamples=10,
)

Only the default method is implemented

 
dcov.test(
    x,
    y,
    index = 0.5,
    R = 10
)

dcor.independence.distance_covariance_test(
    x,
    y,
    exponent=0.5,
    num_resamples=10,
)

dcor.t(x, y)

dcor.independence.distance_correlation_t_statistic(
    x,
    y,
)

dcor.ttest(x, y)

dcor.independence.distance_correlation_t_test(
    x,
    y,
)