98 lines
3.0 KiB
R
98 lines
3.0 KiB
R
#' Multi Linear Multiplication
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#'
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#' \deqn{C\times\{ B_1, ..., B_r \}}{%
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#' C = A x { B1, ..., Br }}
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#'
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#' @param A tensor (multi-linear array)
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#' @param Bs matrix or list of matrices
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#' @param modes integer sequence of the same length as `Bs` specifying the
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#' multiplication axis (defaults to `seq_along(Bs)`)
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#' @param transposed single boolean or boolean vector of same length as \code{Bs}
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#' to transpose the \code{Bs} of matching index before multiplication.
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#'
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#' @examples
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#' # general usage
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#' dimA <- c(3, 17, 19, 2)
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#' dimC <- c(7, 11, 13, 5)
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#' A <- array(rnorm(prod(dimA)), dim = dimA)
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#' Bs <- Map(function(p, q) matrix(rnorm(p * q), p, q), dimC, dimA)
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#' C1 <- mlm(A, Bs)
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#' C2 <- mlm(A, Bs)
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#' C3 <- mlm(A, Bs[c(3, 1, 2, 4)], modes = c(3, 1, 2, 4))
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#' stopifnot(all.equal(C1, C2))
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#' stopifnot(all.equal(C1, C3))
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#'
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#' # selected modes
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#' stopifnot(all.equal(
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#' mlm(A, Bs[2:3], modes = 2:3),
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#' ttm(ttm(A, Bs[[2]], 2), Bs[[3]], 3)
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#' ))
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#'
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#' # analog to matrix multiplication
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#' A <- matrix(rnorm( 6), 2, 3)
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#' B <- matrix(rnorm(12), 3, 4)
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#' C <- matrix(rnorm(20), 5, 4)
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#' stopifnot(all.equal(
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#' A %*% B %*% t(C),
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#' mlm(B, list(A, C))
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#' ))
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#'
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#' # usage of transposed
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#' A <- matrix(rnorm( 6), 2, 3)
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#' B <- matrix(rnorm(15), 3, 5)
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#' C <- matrix(rnorm(35), 5, 7)
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#'
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#' stopifnot(all.equal(
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#' A %*% B %*% C,
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#' mlm(B, list(A, C), transposed = c(FALSE, TRUE))
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#' ))
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#'
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#' # usage with repeated modes (non commutative)
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#' dimA <- c(3, 17, 19, 2)
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#' A <- array(rnorm(prod(dimA)), dim = dimA)
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#' B1 <- matrix(rnorm(9), 3, 3)
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#' B2 <- matrix(rnorm(9), 3, 3)
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#' C <- matrix(rnorm(4), 2, 2)
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#' # same modes do NOT commute
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#' all.equal(
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#' mlm(A, list(B1, B2, C), c(1, 1, 4)), # NOT equal!
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#' mlm(A, list(B2, B1, C), c(1, 1, 4))
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#' )
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#' # but different modes do commute
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#' P1 <- mlm(A, list(C, B1, B2), c(4, 1, 1))
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#' P2 <- mlm(A, list(B1, C, B2), c(1, 4, 1))
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#' P3 <- mlm(A, list(B1, B2, C), c(1, 1, 4))
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#' stopifnot(all.equal(P1, P2))
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#' stopifnot(all.equal(P1, P3))
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#'
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#' # Concatination of MLM is MLM
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#' dimX <- c(4, 8, 6, 3)
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#' dimA <- c(3, 17, 19, 2)
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#' dimB <- c(7, 11, 13, 5)
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#' X <- array(rnorm(prod(dimX)), dim = dimX)
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#' As <- Map(function(p, q) matrix(rnorm(p * q), p, q), dimA, dimX)
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#' Bs <- Map(function(p, q) matrix(rnorm(p * q), p, q), dimB, dimA)
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#' # (X x {A1, A2, A3, A4}) x {B1, B2, B3, B4} = X x {B1 A1, B2 A2, B3 A3, B4 A4}
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#' all.equal(mlm(mlm(X, As), Bs), mlm(X, Map(`%*%`, Bs, As)))
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#'
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#' @export
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mlm <- function(A, Bs, modes = seq_along(Bs), transposed = FALSE) {
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# Collect all matrices in `B`
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Bs <- if (is.matrix(Bs)) list(Bs) else Bs
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# replicate transposition if of length one only
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transposed <- if (length(transposed) == 1) {
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rep(as.logical(transposed), length(Bs))
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} else {
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as.logical(transposed)
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}
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# iteratively apply Tensor Times Matrix multiplication over modes
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for (i in seq_along(modes)) {
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A <- ttm(A, Bs[[i]], modes[i], transposed[i])
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}
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# return result tensor
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A
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}
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