Compute the AIRM Exponential — airm

This function computes the Riemannian exponential map for the Affine-Invariant Riemannian Metric (AIRM).

airm_exp(sigma, v)

Arguments

sigma: A symmetric positive-definite matrix of class dppMatrix, representing the reference point.
v: A tangent vector of class dspMatrix, to be mapped back to the manifold at sigma.

Value

A symmetric positive-definite matrix of class dppMatrix.

Examples

if (requireNamespace("Matrix", quietly = TRUE)) {
  library(Matrix)
  sigma <- diag(2) |>
    Matrix::nearPD() |>
    _$mat |>
    Matrix::pack()
  v <- diag(c(1, 0.5)) |>
    Matrix::symmpart() |>
    Matrix::pack()
  airm_exp(sigma, v)
}
#> 2 x 2 Matrix of class "dppMatrix"
#>          [,1]     [,2]
#> [1,] 2.718282 0.000000
#> [2,] 0.000000 1.648721