R: Inner product in the Hilbert space of U-centered distance...

U_product {energy} | R Documentation

## 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.

### Usage

    U_product(U, V)

### Arguments

`U` | U-centered distance matrix
`V` | U-centered distance matrix

### Details

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.

### Value

`U_product` returns the inner product, a scalar.

### Author(s)

Maria L. Rizzo mrizzo @ bgsu.edu and Gabor J. Szekely

### 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.
http://projecteuclid.org/euclid.aos/1413810731

### Examples

     x <- iris[1:10, 1:4]
     y <- iris[11:20, 1:4]
     M1 <- as.matrix(dist(x))
     M2 <- as.matrix(dist(y))
     U <- U_center(M1)
     V <- U_center(M2)

     U_product(U, V)
     dcovU_stats(M1, M2)

[Package energy version 1.7-6 Index]