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