Info objective

[kaibagley]

Fisher information based objective function, with A and D optimality criterion, and optimises spatially using a user-supplied covariance structure. It is calculated from treatment contrasts, adjusted for nuisance fixed effects like block and intercept.

$$ I = X_1^{\intercal} L X_1 $$

And L removes nuisance effects under a spatial correlation structure from user-supplied $n \times n$ covariance $\Sigma$ and nuisance effects $X_2$

$$ L = \Sigma^{-1} - \Sigma^{-1} X_2 (X_2^{\intercal} \Sigma^{-1} X_2)^{-1} X_2^{\intercal}\Sigma^{-1} $$

With A-optimality $\mathrm{tr}(I^-)$ or contrast-space D-optimality (pseudo determinant since I has rank $\nu - 1$) $-\log \left| I \right|$.

So basically the user specifies the correlation structure they want to use at analysis, such as $AR1 \times AR1$, and the design is optimised to be efficient under that spatial structure. So it should be directly targeting the Cramér-Rao lower bound rather than the adjacency proxy currently used in speed.

[wvjgsuhp]

Thank you for additional objective function.
Please have a look at _pkgdown.yml and see if new functions could be populated where appropriate.
Also, I'd mark helper functions with #' @keywords internal instead of #' @export if they're not expected for users.