# 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

 `1` ```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.

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## Examples

 ```1 2 3 4 5``` ``` 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.