Relocate Tangent Representations to a New Reference Point

Changes the reference point for tangent space representations on a Riemannian manifold.

relocate(old_ref, new_ref, images, met)

Arguments

old_ref

A reference point on the manifold to be replaced. Must be an object of class dppMatrix from the Matrix package.

new_ref

The new reference point on the manifold. Must be an object of class dppMatrix from the Matrix package.

images

A list of tangent representations relative to the old reference point. Each element in the list must be an object of class dspMatrix.

met

A metric object of class rmetric, containing functions for Riemannian operations (logarithmic map, exponential map, vectorization, and inverse vectorization).

Value

A list of tangent representations relative to the new reference point. Each element in the returned list will be an object of class dspMatrix.

Examples

if (requireNamespace("Matrix", quietly = TRUE)) {
  library(Matrix)
  data(airm)
  old_ref <- diag(2) |>
    Matrix::nearPD() |>
    _$mat |>
    Matrix::pack()
  new_ref <- diag(c(2, 3)) |>
    Matrix::nearPD() |>
    _$mat |>
    Matrix::pack()
  images <- list(
    diag(2) |> Matrix::symmpart() |> Matrix::pack(),
    diag(c(1, 0.5)) |> Matrix::symmpart() |> Matrix::pack()
  )
  relocate(old_ref, new_ref, images, airm)
}
#> [[1]]
#> 2 x 2 Matrix of class "dspMatrix"
#>           [,1]       [,2]
#> [1,] 0.6137056  0.0000000
#> [2,] 0.0000000 -0.2958369
#> 
#> [[2]]
#> 2 x 2 Matrix of class "dspMatrix"
#>           [,1]      [,2]
#> [1,] 0.6137056  0.000000
#> [2,] 0.0000000 -1.795837
#>