# R/wrap06rotation.R In Riemann: Learning with Data on Riemannian Manifolds

#### Documented in wrap.rotation

#' Prepare Data on Rotation Group
#'
#' Rotation group, also known as special orthogonal group, is a Riemannian
#' manifold
#' \deqn{SO(p) = \lbrace Q \in \mathbf{R}^{p\times p}~\vert~ Q^\top Q = I, \textrm{det}(Q)=1 \rbrace }
#' where the name originates from an observation that when \eqn{p=2,3} these matrices are rotation of
#' shapes/configurations.
#'
#' @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 rotation matrix.}
#' \item{list}{a length-\eqn{n} list whose elements are \eqn{(p\times p)} rotation matrices.}
#' }
#'
#' @return a named \code{riemdata} S3 object containing
#' \describe{
#'   \item{data}{a list of \eqn{(p\times p)} rotation matrices.}
#'   \item{size}{size of each rotation matrix.}
#'   \item{name}{name of the manifold of interests, \emph{"rotation"}}
#' }
#'
#'
#' @examples
#' #-------------------------------------------------------------------
#' #                 Checker for Two Types of Inputs
#' #-------------------------------------------------------------------
#' ## DATA GENERATION
#' d1 = array(0,c(3,3,5))
#' d2 = list()
#' for (i in 1:5){
#'   single  = qr.Q(qr(matrix(rnorm(9),nrow=3)))
#'   d1[,,i] = single
#'   d2[[i]] = single
#' }
#'
#' ## RUN
#' test1 = wrap.rotation(d1)
#' test2 = wrap.rotation(d2)
#'
#' @concept wrapper
#' @export
wrap.rotation <- function(input){
## TAKE EITHER 3D ARRAY OR A LIST
#  1. data format
if (is.array(input)){
if (!check_3darray(input, symmcheck=FALSE)){
stop("* wrap.rotation : 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.rotation : 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.rotation : elements are not of same size.")
}
#  3. check and transform to Stiefel
N = length(tmpdata)
for (n in 1:N){
tmpcheck     = single_rotcheck(tmpdata[[n]], n)
tmpdata[[n]] = tmpdata[[n]]
}

## WRAP AND RETURN THE S3 CLASS
output = list()
output$data = tmpdata output$size = dim(tmpdata[[1]])
output\$name = "rotation"
return(structure(output, class="riemdata"))
}
#' @keywords internal
#' @noRd
single_rotcheck <- function(x, id=0){
p = nrow(x)
if (nrow(x)!=ncol(x)){
stop(paste0("* wrap.rotation : ",id,"-th element is not a square matrix."))
}
if ((norm((t(x)%*%x)-diag(p),"F")/sqrt(p) >= 1e-10)){
stop(paste0("* wrap.rotation : ",id,"-th element does not satisfy X'*X = I."))
}
if (abs(base::det(x)-1) >= 1e-10){
stop(paste0("* wrap.rotation : ",id,"-th element's determinant is not close to 1."))
}
return(TRUE)
}


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