41 lines
1.2 KiB
R
41 lines
1.2 KiB
R
#' Approximates kronecker product decomposition.
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#'
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#' Approximates the matrices `A` and `B` such that
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#' C = A %x% B
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#' with `%x%` the kronecker product of the matrixes `A` and `B`
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#' of dimensions `dimA` and `dimB` respectively.
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#'
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#' @param C desired kronecker product result.
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#' @param dimA length 2 vector of dimensions of \code{A}.
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#' @param dimB length 2 vector of dimensions of \code{B}.
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#'
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#' @return list with attributes `A` and `B`.
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#'
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#' @examples
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#' A <- matrix(seq(14), 7, 2)
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#' B <- matrix(c(T, F), 3, 4)
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#' C <- kronecker(A, B) # the same as 'C <- A %x% B'
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#' approx.kronecker(C, dim(A), dim(B))
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#'
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#' @seealso C.F. Van Loan / Journal of Computational and Applied Mathematics
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#' 123 (2000) 85-100 (pp. 93-95)
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#'
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#' @imports RSpectra
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#'
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approx.kronecker <- function(C, dimA, dimB) {
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dim(C) <- c(dimB[1L], dimA[1L], dimB[2L], dimA[2L])
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R <- aperm(C, c(2L, 4L, 1L, 3L))
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dim(R) <- c(prod(dimA), prod(dimB))
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svdR <- try(RSpectra::svds(R, 1L), silent = TRUE)
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if (is(svdR, 'try-error')) {
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svdR <- svd(R, 1L, 1L)
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}
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return(list(
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A = array(sqrt(svdR$d[1]) * svdR$u, dimA),
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B = array(sqrt(svdR$d[1]) * svdR$v, dimB)
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))
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}
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