41 lines
1.2 KiB
R
41 lines
1.2 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 column 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 `(2, n * (n - 1) / 2)` for a argument of lenght `n`.
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#' @keywords internal
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#' @examples
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#' elem.pairs(seq.int(2, 5))
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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 <- rbind(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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