Description Usage Arguments References See Also Examples
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
.
1 | Expm(P, H)
|
P |
a Hermitian positive definite matrix. |
H |
a Hermitian matrix (of equal dimension as |
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)
|
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