Fixed residual covariance for a GLS competitor

Evaluates the convolution covariance \(\boldsymbol{\Sigma}(\boldsymbol{p})=\sum_j p_j^2\boldsymbol{\Sigma}_j\) at a known composition (default the barycentre \(p_j=1/J\)) and optionally keeps only the diagonal. That matrix does not depend on the unknown \(\boldsymbol{p}\) at fit time. Do not copy it into every slice of a DeCovarT tensor: that would yield \(\|p\|_2^2\boldsymbol{\Sigma}_{\mathrm{GLS}}\), which still depends on \(p\).

Usage

fixed_gls_covariance(Sigma, p = NULL, diagonal = TRUE)

Arguments

Sigma

Array \(G\times G\times J\) of cell-type covariances.

p

Optional composition of length \(J\); default \((1/J,\ldots,1/J)\).

diagonal

If TRUE (default), return \(\operatorname{diag}\{\boldsymbol{\Sigma}(\boldsymbol{p})\}\).

Value

A \(G\times G\) covariance matrix.

See also

deconvolute_ratios_gls()

Examples

Sigma <- array(c(diag(2), 2 * diag(2)), dim = c(2, 2, 2))
fixed_gls_covariance(Sigma)
#>      [,1] [,2]
#> [1,] 0.75 0.00
#> [2,] 0.00 0.75