2022-10-06 12:25:40 +00:00
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#' Half vectorization of a matrix (lower part)
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#' @export
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vech <- function(A) A[lower.tri(A, diag = TRUE)]
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#' @export
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vech.index <- function(p) which(.row(c(p, p)) >= .col(c(p, p)))
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#' @export
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vech.pinv.index <- function(p) {
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index <- matrix(NA_integer_, p, p)
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index[lower.tri(index, diag = TRUE)] <- seq_len(p * (p + 1L) / 2L)
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index[upper.tri(index)] <- t(index)[upper.tri(index)]
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index
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}
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#' pseudo inserse of the half vectorization
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#'
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#' @examples
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#' # only valid for symmetric matrices
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#' A <- matrix(rnorm(4^2), 4)
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#' A <- A + t(A)
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#' all.equal(A, vech.pinv(vech(A)))
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#'
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#' @export
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vech.pinv <- function(a) {
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# determin original dimensions
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p <- as.integer((sqrt(8 * length(a) + 1) - 1) / 2)
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stopifnot(p * (p + 1L) == 2L * length(a))
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# de-vectorized matrix
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matrix(a[vech.pinv.index(p)], p, p)
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}
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2023-11-14 13:35:43 +00:00
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# vech <- function(A) {
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# stopifnot(all(nrow(A) == dim(A)))
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# axis <- seq_len(nrow(A))
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# grid <- expand.grid(c(list(rev(axis)), rep(list(axis), length(dim(A)) - 1)))
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# A[rowSums(grid - 1) < nrow(A)]
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# }
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# p <- 4
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# X <- matrix(rnorm(p^2), p)
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# vech(outer(X, X))
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# vech(outer(c(X), c(X)))
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# sort(unique(c(sym(outer(X, X)))))
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# sort(vech(sym(outer(X, X))))
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# # (I <- matrix(c(
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# # 1, 1, 1,
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# # 2, 1, 1,
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# # 3, 1, 1,
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# # 2, 2, 1,
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# # 3, 2, 1,
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# # 3, 3, 1,
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# # 2, 1, 2,
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# # 3, 1, 2,
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# # 3, 2, 2,
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# # 3, 1, 3
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# # ), ncol = 3, byrow = TRUE))
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# # ((I - 1) %*% nrow(A)^(seq_along(dim(A)) - 1) + 1)
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# # p <- 3
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# # ord <- 4
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# # A <- array(seq_len(p^ord), rep(p, ord))
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# # axis <- seq_len(nrow(A))
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# # grid <- expand.grid(c(list(rev(axis)), rep(list(axis), length(dim(A)) - 1)))
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# # array(rowSums(grid - 1), dim(A))
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# # A[rowSums(grid - 1) < nrow(A)]
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# # apply(indices, 1, function(i) do.call(`[`, c(list(A), as.list(i))))
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