Build cell-type-specific covariances from precision slices

For each cell type \(j\), inverts \(\boldsymbol{\Omega}_j\) to \(\boldsymbol{\Sigma}_j=\boldsymbol{\Omega}_j^{-1}\) (via qr.solve()) and stacks the result as a \(G\times G\times J\) array. If a slice is not numerically SPD, or if the inverse fails Cholesky, a further uniform spectral shift is applied to that precision (off-diagonal support unchanged). Precisions need not be shared across cell types.

Usage

build_covariance_array_from_precision(precision_array)

Arguments

precision_array

Symmetric positive-definite array \((\boldsymbol{\Omega}_j)_{j}\in\mathcal{M}_{G\times G\times J}\).

Value

Numeric array of dimension \(G\times G\times J\).

Examples

A <- generate_random_network_skeleton(6L, "hub")
W <- assign_iid_signed_weights(A)
Omega <- build_normalised_precision(W, precision_shift = 0.2)
arr <- array(Omega, dim = c(6, 6, 1))
dim(build_covariance_array_from_precision(arr))
#> [1] 6 6 1