R/wrap02spd.R In Riemann: Learning with Data on Riemannian Manifolds

Documented in wrap.spd

#' Prepare Data on Symmetric Positive-Definite (SPD) Manifold
#'
#' The collection of symmetric positive-definite matrices is a well-known example
#' of matrix manifold. It is defined as
#' \deqn{\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 \code{wrap.spdk}.
#'
#' @param input SPD data matrices to be wrapped as \code{riemdata} class. Following inputs are considered,
#' \describe{
#' \item{array}{an \eqn{(p\times p\times n)} array where each slice along 3rd dimension is a SPD matrix.}
#' \item{list}{a length-\eqn{n} list whose elements are \eqn{(p\times p)} SPD matrices.}
#' }
#'
#' @return a named \code{riemdata} S3 object containing
#' \describe{
#'   \item{data}{a list of \eqn{(p\times p)} correlation matrices.}
#'   \item{size}{size of each correlation matrix.}
#'   \item{name}{name of the manifold of interests, \emph{"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)
#'
#' @concept wrapper
#' @export
wrap.spd <- function(input){
## TAKE EITHER 3D ARRAY OR A LIST
#  1. data format
if (is.array(input)){
if (!check_3darray(input, symmcheck=TRUE)){
stop("* wrap.spd : input does not follow the size requirement as described.")
}
N = dim(input)[3]
tmpdata = list()
for (n in 1:N){
tmpdata[[n]] = input[,,n]
}
} else if (is.list(input)){
tmpdata = input
} else {
stop("* wrap.spd : input should be either a 3d array or a list.")
}
#  2. check all same size
if (!check_list_eqsize(tmpdata, check.square=TRUE)){
stop("* wrap.spd : elements are not of same size.")
}
#  3. check
N = length(tmpdata)
for (n in 1:N){
tmpdata[[n]] = check_spd(tmpdata[[n]], n)
}

# WRAP AND RETURN THE S3 CLASS
output = list()
output$data = tmpdata output$size = dim(tmpdata[[1]])
output\$name = "spd"
return(structure(output, class="riemdata"))
}
#' @keywords internal
#' @noRd
check_spd <- function(x, id){
p = nrow(x)
cond1 = (nrow(x)==ncol(x))
cond2 = (round(mat_rank(x))==p) # full-rank
cond3 = isSymmetric(x)
if (cond1&&cond2&&cond3){
return(x)
} else {
remainder = (id%%10)
if (remainder==1){
stop(paste0(" wrap.spd : ",id,"st object is not a valid SPD object."))
} else if (remainder==2){
stop(paste0(" wrap.spd : ",id,"nd object is not a valid SPD object."))
} else if (remainder==3){
stop(paste0(" wrap.spd : ",id,"rd object is not a valid SPD object."))
} else {
stop(paste0(" wrap.spd : ",id,"th object is not a valid SPD object."))
}
}
}


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Riemann documentation built on June 20, 2021, 5:07 p.m.