Bulk mixture covariance \(\boldsymbol{\Sigma}(\boldsymbol{p})\)

Assembles the conditional covariance of the Gaussian convolution $$ \boldsymbol{\Sigma}(\boldsymbol{p}) =\sum_{j=1}^{J}p_j^{2}\,\boldsymbol{\Sigma}_j, $$ stored as slices of the array Sigma.

Usage

.compute_global_variance(p, Sigma)

Arguments

p

Numeric vector \(\boldsymbol{p}\in\mathbb{R}^{J}\).

Sigma

Array of cell-type covariances in \(\mathcal{M}_{G\times G\times J}\).

Value

Symmetric matrix \(\boldsymbol{\Sigma}(\boldsymbol{p})\in\mathcal{M}_{G\times G}\).

Examples

p <- c(0.6, 0.4)
Sigma <- array(c(diag(2), diag(2)), dim = c(2, 2, 2))
.compute_global_variance(p, Sigma)
#>      [,1] [,2]
#> [1,] 0.52 0.00
#> [2,] 0.00 0.52