Trace of the precision times a matrix, \(\operatorname{tr}(\boldsymbol{\Omega}(\boldsymbol{p})\mathbf{S})\)

Computes \(\operatorname{tr}(\boldsymbol{\Sigma}(\boldsymbol{p})^{-1} \mathbf{S})\) through solves only, never materialising the dense precision. This is the trace term that appears in the analytic gradient and Hessian.

Usage

sigma_trace_precision_times(backend, p, S)

Arguments

backend

A new_decovart_covariance() object.

p

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

S

Numeric \(G\times G\) matrix (typically a cell-type covariance slice \(\boldsymbol{\Sigma}_j\)).

Value

Scalar trace.

See also

sigma_solve()

Examples

Sigma <- array(c(diag(2), diag(2)), dim = c(2, 2, 2))
cov <- new_decovart_covariance(Sigma, "dense")
sigma_trace_precision_times(cov, c(0.6, 0.4), Sigma[, , 1])
#> [1] 3.846154