All functions return a square symmetric matrix.

`Dcenter`

returns a matrix

$$A_{ij}=a_{ij} - \bar a_{i.} - \bar a_{.j} + \bar a_{..}$$

as in classical multidimensional scaling. `Ucenter`

returns a matrix

$$\tilde A_{ij}=a_{ij} - \frac{a_{i.}}{n-2}
- \frac{a_{.j}}{n-2} + \frac{a_{..}}{(n-1)(n-2)},\quad i \neq j,$$

with zero diagonal,
and this is the double centering applied in `pdcov`

and

`pdcor`

as well as the unbiased dCov and bias corrected
dCor statistics.