80 lines
2.3 KiB
R
80 lines
2.3 KiB
R
#' Penalysed Orthogonal Iteration.
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#'
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#' @param lambda Default: 0.75 * lambda_max for FastPOI-C method.
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#'
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#' @note use.C required 'poi.so' beeing dynamicaly loaded.
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#' dyn.load('../tensor_predictors/poi.so')
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POI <- function(A, B, d,
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lambda = 0.75 * sqrt(max(rowSums(Delta^2))),
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update.tol = 1e-3,
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tol = 100 * .Machine$double.eps,
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maxit = 400L,
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maxit.outer = maxit,
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maxit.inner = maxit,
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use.C = FALSE,
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method = 'FastPOI-C') {
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# TODO:
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stopifnot(method == 'FastPOI-C')
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if (nrow(A) < 100) {
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Delta <- eigen(A, symmetric = TRUE)$vectors[, 1:d, drop = FALSE]
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} else {
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Delta <- try(RSpectra::eigs_sym(A, d)$vectors, silent = TRUE)
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if (is(Delta, 'try-error')) {
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Delta <- eigen(A, symmetric = TRUE)$vectors[1:d, , drop = FALSE]
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}
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}
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# Set initial value.
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Z <- Delta
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# Step 1: Optimization.
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# The "inner" optimization loop, aka repeated coordinate optimization.
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if (use.C) {
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Z <- .Call('FastPOI_C_sub', A, B, Delta, lambda, as.integer(maxit.inner),
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PACKAGE = 'poi')
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} else {
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p <- nrow(Z)
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for (iter.inner in 1:maxit.inner) {
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Zold <- Z
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for (g in 1:p) {
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a <- Delta[g, ] - B[g, ] %*% Z + B[g, g] * Z[g, ]
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a_norm <- sqrt(sum(a^2))
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if (a_norm > lambda) {
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Z[g, ] <- a * ((1 - lambda / a_norm) / B[g, g])
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} else {
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Z[g, ] <- 0
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}
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}
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if (norm(Z - Zold, 'F') < update.tol) {
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break;
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}
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}
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}
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# Step 2: QR decomposition.
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if (d == 1L) {
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Z_norm <- sqrt(sum(Z^2))
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if (Z_norm < tol) {
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Q <- matrix(0, p, d)
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} else {
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Q <- Z / Z_norm
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}
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} else {
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# Detect zero columns.
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zeroColumn <- colSums(abs(Z)) < tol
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if (all(zeroColumn)) {
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Q <- matrix(0, p, d)
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} else if (any(zeroColumn)) {
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Q <- matrix(0, p, d)
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Q[, !zeroColumn] <- qr.Q(qr(Z))
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} else {
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Q <- qr.Q(qr(Z))
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}
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}
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return(list(Z = Z, Q = Q, iter.inner = if (use.C) NA else iter.inner,
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lambda = lambda))
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}
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