| pdDist {pdSpecEst} | R Documentation |
Compute distance between two HPD matrices
Description
pdDist calculates a distance between two Hermitian PD matrices.
Usage
pdDist(A, B, metric = "Riemannian")
Arguments
A, B |
Hermitian positive definite matrices (of equal dimension). |
metric |
the distance measure, one of |
Details
Available distance measures between two HPD matrices are: (i) the affine-invariant Riemannian distance (default) as in
e.g., (Bhatia 2009)[Chapter 6] or (Pennec et al. 2006); (ii) the Log-Euclidean distance,
the Euclidean distance between matrix logarithms; (iii) the Cholesky distance, the Euclidean distance between Cholesky decompositions;
(iv) the Euclidean distance; (v) the root-Euclidean distance; and (vi) the Procrustes distance as in (Dryden et al. 2009).
In particular, pdDist generalizes the function shapes::distcov, to compute the distance between two symmetric positive
definite matrices, in order to compute the distance between two Hermitian positive definite matrices.
References
Bhatia R (2009).
Positive Definite Matrices.
Princeton University Press, New Jersey.
Dryden I, Koloydenko A, Zhou D (2009).
“Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging.”
The Annals of Applied Statistics, 3(3), 1102–1123.
Pennec X, Fillard P, Ayache N (2006).
“A Riemannian framework for tensor computing.”
International Journal of Computer Vision, 66(1), 41–66.
Examples
a <- matrix(complex(real = rnorm(9), imaginary = rnorm(9)), nrow = 3)
A <- t(Conj(a)) %*% a
b <- matrix(complex(real = rnorm(9), imaginary = rnorm(9)), nrow = 3)
B <- t(Conj(b)) %*% b
pdDist(A, B) ## Riemannian distance