Logm {pdSpecEst}

Riemannian HPD logarithmic map

Description

Logm(P, Q) computes the projection of a Hermitian PD matrix Q in the manifold of HPD matrices equipped with the affine-invariant Riemannian metric to the tangent space attached at the Hermitian PD matrix P via the logarithmic map as in e.g., (Pennec et al. 2006). This is the unique inverse of the exponential map Expm.

Usage

Logm(P, Q)

Arguments

P

a Hermitian positive definite matrix.

Q

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

References

Pennec, X. (2006). Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements. Journal of Mathematical Imaging and Vision 25(1), 127-154.

See Also

Expm, pdParTrans

Examples

 ## Generate two random HPD matrices
 q <- matrix(complex(real = rnorm(9), imaginary = rnorm(9)), nrow = 3)
 Q <- t(Conj(q)) %*% q
 p <- matrix(complex(real = rnorm(9), imaginary = rnorm(9)), nrow = 3)
 P <- t(Conj(p)) %*% p
 ## Compute logarithmic map
 Logm(P, Q)