Expm: Riemannian HPD exponential map In pdSpecEst: An Analysis Toolbox for Hermitian Positive Definite Matrices

Description

`Expm(P, H)` computes the projection of a Hermitian matrix `H` from the tangent space at a Hermitian PD matrix `P` to the manifold of Hermitian PD matrices equipped with the affine-invariant Riemannian metric via the exponential map as in e.g., \insertCitePFA05pdSpecEst. This is the unique inverse of the Riemannian logarithmic map `Logm`.

Usage

 `1` ```Expm(P, H) ```

Arguments

 `P` a Hermitian positive definite matrix. `H` a Hermitian matrix (of equal dimension as `P`).

References

\insertAllCited

`Logm, pdParTrans`
 ```1 2 3 4 5 6 7 8 9``` ``` ## Generate random Hermitian matrix H <- matrix(complex(real = rnorm(9), imaginary = rnorm(9)), nrow = 3) diag(H) <- rnorm(3) H[lower.tri(H)] <- t(Conj(H))[lower.tri(H)] ## Generate random HPD matrix p <- matrix(complex(real = rnorm(9), imaginary = rnorm(9)), nrow = 3) P <- t(Conj(p)) %*% p ## Compute exponential map Expm(P, H) ```