Expm {pdSpecEst}

Riemannian HPD exponential map

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., (Pennec et al. 2006). This is the unique inverse of the Riemannian logarithmic map Logm.

Usage

Expm(P, H)

Arguments

P

a Hermitian positive definite matrix.

H

a Hermitian matrix (of equal dimension as P).

References

Pennec X, Fillard P, Ayache N (2006). “A Riemannian framework for tensor computing.” International Journal of Computer Vision, 66(1), 41–66.

See Also

Logm, pdParTrans

Examples

 ## 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)