Mean pairwise AIRM distance of component covariances

Mean pairwise AIRM distance of component covariances

Usage

compute_average_riemannian(true_theta, J = NULL)

Arguments

true_theta

List validated by check_true_theta(): mu (\(G\times J\)), sigma (\(G\times G\times J\)), and optionally p (length \(J\) or \(J\times N\)). If p is missing it is set to \((1/J,\ldots,1/J)\).

J

Number of cell types. Defaults to the third dimension of sigma.

Value

Scalar average of \(d_R(\Sigma_j,\Sigma_\ell)\) over \(j<\ell\).

See also

spd_affine_invariant_distance()

Examples

a <- diag(2)
b <- matrix(c(2, 0.5, 0.5, 1), nrow = 2)
theta <- list(
  mu = cbind(c(0, 0), c(1, 0)),
  sigma = array(c(a, b), dim = c(2, 2, 2))
)
compute_average_riemannian(theta)
#> [1] 0.8249946
# J = 2 has a single pair, so the average equals the pairwise AIRM.
all.equal(
  compute_average_riemannian(theta),
  spd_affine_invariant_distance(a, b)
)
#> [1] TRUE