daniel
c4a93d25fa
add: if for cond.threshold if non-finite, allows to disable regularization, fix: TSIR's mode-wise sample covariance scaling factor
55 lines
1.8 KiB
R
55 lines
1.8 KiB
R
#' Subspace distance
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#'
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#' @param As,Bs Basis matrices or list of Kronecker components of basis matrices
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#' as representations of elements of the Grassmann manifold.
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#' @param is.ortho Boolean to specify if \eqn{A} and \eqn{B} are semi-orthogonal.
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#' If false, the projection matrices are computed as
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#' \deqn{P_A = A (A' A)^{-1} A'}
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#' otherwise just \eqn{P_A = A A'} since \eqn{A' A} is the identity.
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#' @param normalize Boolean to specify if the distance shall be normalized.
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#' Meaning, the maximal distance scaled to be \eqn{1} independent of dimensions.
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#'
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#' @seealso
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#' K. Ye and L.-H. Lim (2016) "Schubert varieties and distances between
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#' subspaces of different dimensions" <arXiv:1407.0900>
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#'
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#' @export
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dist.subspace <- function (As, Bs, is.ortho = FALSE, normalize = FALSE,
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tol = sqrt(.Machine$double.eps)
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) {
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As <- if (is.list(As)) Map(as.matrix, As) else list(as.matrix(As))
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Bs <- if (is.list(Bs)) Map(as.matrix, Bs) else list(as.matrix(Bs))
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if (!is.ortho) {
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As <- Map(function(A) {
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qrA <- qr(A, tol)
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if (qrA$rank < ncol(A)) {
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qr.Q(qrA)[, abs(diag(qr.R(qrA))) > tol, drop = FALSE]
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} else {
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qr.Q(qrA)
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}
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}, As)
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Bs <- Map(function(B) {
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qrB <- qr(B, tol)
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if (qrB$rank < ncol(B)) {
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qr.Q(qrB)[, abs(diag(qr.R(qrB))) > tol, drop = FALSE]
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} else {
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qr.Q(qrB)
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}
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}, Bs)
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}
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rankA <- prod(sapply(As, ncol))
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rankB <- prod(sapply(Bs, ncol))
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c <- if (normalize) {
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rankSum <- rankA + rankB
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sqrt(1 / max(1, min(rankSum, 2 * prod(sapply(As, nrow)) - rankSum)))
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} else {
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1
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}
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s <- prod(mapply(function(A, B) sum(crossprod(A, B)^2), As, Bs))
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c * sqrt(max(0, rankA + rankB - 2 * s))
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}
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