64 lines
1.9 KiB
R
64 lines
1.9 KiB
R
#' Samples uniform from the Stiefel Manifold
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#'
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#' @param p row dim.
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#' @param q col dim.
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#' @return `(p, q)` semi-orthogonal matrix
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#' @examples
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#' V <- rStiefel(6, 4)
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#' @export
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rStiefl <- function(p, q) {
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return(qr.Q(qr(matrix(rnorm(p * q, 0, 1), p, q))))
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}
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#' Null space basis of given matrix `V`
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#'
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#' @param V `(p, q)` matrix
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#' @return Semi-orthogonal `(p, p - q)` matrix spaning the null space of `V`.
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#' @keywords internal
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#' @export
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null <- function(V) {
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tmp <- qr(V)
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set <- if(tmp$rank == 0L) seq_len(ncol(V)) else -seq_len(tmp$rank)
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return(qr.Q(tmp, complete=TRUE)[, set, drop=FALSE])
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}
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#' Creates a (numeric) matrix where each row contains
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#' an element to element matching.
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#' @param elements numeric vector of elements to match
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#' @return matrix of size `(n * (n - 1) / 2, 2)` for a argument of lenght `n`.
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#' @keywords internal
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#' @export
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elem.pairs <- function(elements) {
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# Number of elements to match.
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n <- length(elements)
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# Create all combinations.
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pairs <- cbind(rep(elements, each=n), rep(elements, n))
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# Select unique combinations without self interaction.
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return(pairs[pairs[, 1] < pairs[, 2], ])
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}
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#' Apply function to pairs of matrix rows or columns.
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#'
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#' \code{row.pair.apply} applies \code{FUN} to each unique row pair without self
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#' interaction while \code{col.pair.apply} does the same for columns.
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#' @param X Matrix.
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#' @param FUN Function to apply to each pair.
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#' @examples
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#' X <- matrix(seq(12), 4, 3)
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#' # matrix containing all row to row differences.
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#' row.pair.apply(X, `-`)
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#' @aliases row.pair.apply, col.pair.apply
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#' @keywords internal
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#' @export
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row.pair.apply <- function(X, FUN) {
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pairs <- elem.pairs(seq(nrow(X)))
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return(FUN(X[pairs[, 1], ], X[pairs[, 2], ]))
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}
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#' @rdname row.pair.apply
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#' @keywords internal
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#' @export
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col.pair.apply <- function(X, FUN) {
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pairs <- elem.pairs(seq(ncol(X)))
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return(FUN(X[, pairs[, 1]], X[, pairs[, 2]]))
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}
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