wrap.spd {Riemann}

Prepare Data on Symmetric Positive-Definite (SPD) Manifold

Description

The collection of symmetric positive-definite matrices is a well-known example of matrix manifold. It is defined as

\mathcal{S}_{++}^p = \lbrace X \in \mathbf{R}^{p\times p} ~\vert~ X^\top = X,~ \textrm{rank}(X)=p \rbrace

where the rank condition means it is strictly positive definite. Please note that the geometry involving semi-definite matrices is considered in wrap.spdk.

Usage

wrap.spd(input)

Arguments

input

SPD data matrices to be wrapped as riemdata class. Following inputs are considered,

array

an (p\times p\times n) array where each slice along 3rd dimension is a SPD matrix.

list

a length-n list whose elements are (p\times p) SPD matrices.

Value

a named riemdata S3 object containing

data

a list of (p\times p) SPD matrices.

size

size of each SPD matrix.

name

name of the manifold of interests, "spd"

Examples

#-------------------------------------------------------------------
#                 Checker for Two Types of Inputs
#
#  Generate 5 observations; empirical covariance of normal observations.
#-------------------------------------------------------------------
#  Data Generation
d1 = array(0,c(3,3,5))
d2 = list()
for (i in 1:5){
  dat = matrix(rnorm(10*3),ncol=3)
  d1[,,i] = stats::cov(dat)
  d2[[i]] = d1[,,i]
}

#  Run
test1 = wrap.spd(d1)
test2 = wrap.spd(d2)