# R/wrap08spdk.R In Riemann: Learning with Data on Riemannian Manifolds

#### Documented in wrap.spdk

#' Prepare Data on SPD Manifold of Fixed-Rank
#'
#' When \eqn{(p\times p)} SPD matrices are of fixed-rank \eqn{k < p}, they form
#' a geometric structure represented by \eqn{(p\times k)} matrices,
#' \deqn{SPD(k,p) = \lbrace X \in \mathbf{R}^{(p\times p)}~\vert~ Y Y^\top = X, \textrm{rank}(X) = k \rbrace}
#' It's key difference from \eqn{\mathcal{S}_{++}^p} is that all matrices should be
#' of fixed rank \eqn{k} where \eqn{k} is usually smaller than \eqn{p}. Inputs are
#' given as \eqn{(p\times p)} matrices with specified \eqn{k} and \code{wrap.spdk}
#' automatically decomposes input square matrices into rank-\eqn{k} representation matrices.
#'
#' @param input data matrices to be wrapped as \code{riemdata} class. Following inputs are considered,
#' \describe{
#' \item{array}{a \eqn{(p\times p\times n)} array where each slice along 3rd dimension is a rank-\eqn{k} matrix.}
#' \item{list}{a length-\eqn{n} list whose elements are \eqn{(p\times p)} matrices of rank-\eqn{k}.}
#' }
#' @param k rank of the SPD matrices.
#'
#' @return a named \code{riemdata} S3 object containing
#' \describe{
#'   \item{data}{a list of \eqn{(p\times k)} representation of the corresponding rank-\eqn{k} SPSD matrices.}
#'   \item{size}{size of each representation matrix.}
#'   \item{name}{name of the manifold of interests, \emph{"spdk"}}
#' }
#'
#' @examples
#' #-------------------------------------------------------------------
#' #                 Checker for Two Types of Inputs
#' #-------------------------------------------------------------------
#' #  Data Generation
#' d1 = array(0,c(10,10,3))
#' d2 = list()
#' for (i in 1:3){
#'   dat = matrix(rnorm(10*10),ncol=10)
#'   d1[,,i] = stats::cov(dat)
#'   d2[[i]] = d1[,,i]
#' }
#'
#' #  Run
#' test1 = wrap.spdk(d1, k=2)
#' test2 = wrap.spdk(d2, k=2)
#'
#'
#' @references
#' \insertRef{journee_lowrank_2010}{Riemann}
#'
#' @concept wrapper
#' @export
wrap.spdk <- function(input, k){
## TAKE EITHER 3D ARRAY OR A LIST
#  1. data format
if (is.array(input)){
if (!check_3darray(input, symmcheck=FALSE)){
stop("* wrap.spdk : 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.spdk : 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.spdk : elements are not of same size.")
}
#  3. check and transform
N = length(tmpdata)
K = round(k)
if ((K<1)||(K>nrow(tmpdata[[1]]))){
stop("* wrap.spdk : target rank 'k' should be in [1,p]. For two extreme cases, use other geometries.")
}
for (n in 1:N){
tmpdata[[n]] = single_spdkcheck(tmpdata[[n]], n, K)
}

## WRAP AND RETURN THE S3 CLASS
output = list()
output$data = tmpdata output$size = dim(tmpdata[[1]])
output$name = "spdk" return(structure(output, class="riemdata")) } #' @keywords internal #' @noRd single_spdkcheck <- function(x, id, k){ p = nrow(x) if (!(nrow(x)==ncol(x))){ stop(paste0("* wrap.spdk : ",id,"-th element is not a square matrix.")) } if (!isSymmetric(x)){ stop(paste0("* wrap.spdk : ",id,"-th element is not a symmetric matrix.")) } xrank = round(mat_rank(x)) eigx = base::eigen(x) if (xrank >= k){ output = eigx$vectors[,1:k]%*%sqrt(diag(eigx\$values[1:k]))
} else {
stop(paste0("* wrap.spdk : ",id,"-th element is rank deficient."))
}
return(output)
}


## Try the Riemann package in your browser

Any scripts or data that you put into this service are public.

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