U_product: Inner product in the Hilbert space of U-centered
distance matrices

Description

Stand-alone function to compute the inner product in the
Hilbert space of U-centered distance matrices, as in the definition of
partial distance covariance.

Note that pdcor, etc. functions include the centering and
projection operations, so that these stand alone versions are not
needed except in case one wants to check the internal computations.

Exported from U_product.cpp.

References

Szekely, G.J. and Rizzo, M.L. (2014),
Partial Distance Correlation with Methods for Dissimilarities,
Annals of Statistics, Vol. 42, No. 6, pp. 2382-2412.