50 lines
1.5 KiB
R
50 lines
1.5 KiB
R
#' Subspace distance
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#'
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#' @param A,B Basis matrices as representations of elements of the Grassmann
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#' 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 (A, B, is.ortho = FALSE, normalize = FALSE,
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tol = sqrt(.Machine$double.eps)
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) {
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if (!is.matrix(A)) A <- as.matrix(A)
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if (!is.matrix(B)) B <- as.matrix(B)
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if (!is.ortho) {
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qrA <- qr(A, tol)
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if (qrA$rank < ncol(A)) {
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A <- qr.Q(qrA)[, abs(diag(qr.R(qrA))) > tol, drop = FALSE]
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} else {
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A <- qr.Q(qrA)
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}
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qrB <- qr(B, tol)
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if (qrB$rank < ncol(B)) {
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B <- qr.Q(qrB)[, abs(diag(qr.R(qrB))) > tol, drop = FALSE]
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} else {
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B <- qr.Q(qrB)
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}
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}
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PA <- tcrossprod(A, A)
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PB <- tcrossprod(B, B)
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if (normalize) {
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rankSum <- ncol(A) + ncol(B)
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c <- 1 / sqrt(max(1, min(rankSum, 2 * nrow(A) - rankSum)))
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} else {
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c <- sqrt(2)
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}
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c * norm(PA - PB, type = "F")
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}
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