pdDist: Compute distance between two HPD matrices

In pdSpecEst: An Analysis Toolbox for Hermitian Positive Definite 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 'Riemannian', 'logEuclidean', 'Cholesky', 'Euclidean', 'rootEuclidean' or 'Procrustes'. Defaults to 'Riemannian'.

Details

Available distance measures between two HPD matrices are: (i) the affine-invariant Riemannian distance (default) as in e.g., \insertCiteB09pdSpecEst[Chapter 6] or \insertCitePFA05pdSpecEst; (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 \insertCiteD09pdSpecEst. 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

\insertAllCited

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

pdSpecEst documentation built on Jan. 8, 2020, 5:08 p.m.