tensor_predictors/tensorPredictors/R/dist_projection.R

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2023-11-14 13:35:43 +00:00
#' Projection Distance of two matrices
#'
#' Defined as sine of the maximum principal angle between the column spaces
#' of the matrices
#' max{ sin theta_i, i = 1, ..., min(d1, d2) }
#' In case of rank(A) = rank(B) this measure is equivalent to
#' || A A' - B B' ||_2
#' where ||.||_2 is the spectral norm (max singular value).
#'
#' @param A,B matrices of size \eqn{p\times d_1} and \eqn{p\times d_2}.
#'
#' @export
dist.projection <- function(A, B, is.ortho = FALSE,
tol = sqrt(.Machine$double.eps)
) {
if (!is.matrix(A)) A <- as.matrix(A)
if (!is.matrix(B)) B <- as.matrix(B)
if (!is.ortho) {
qrA <- qr(A, tol)
rankA <- qrA$rank
A <- qr.Q(qrA)[, seq_len(qrA$rank), drop = FALSE]
qrB <- qr(B, tol)
rankB <- qrB$rank
B <- qr.Q(qrB)[, seq_len(qrB$rank), drop = FALSE]
} else {
rankA <- ncol(A)
rankB <- ncol(B)
}
if (rankA == 0 || rankB == 0) {
return(as.double(rankA != rankB))
} else if (rankA == 1 && rankB == 1) {
sigma.min <- min(abs(sum(A * B)), 1)
} else {
sigma.min <- min(La.svd(crossprod(A, B), 0, 0)$d, 1)
}
if (sigma.min < 0.5) {
sin(acos(sigma.min))
} else {
cos(asin(sigma.min))
}
}