rpca_alm <- function(M, tol=1e-6) {
mdim <- dim(M)
mu <- prod(mdim) / (4.0 * sum(abs(M)))
lamb <- 1/sqrt(max(mdim))
L <- matrix(0, dim(M))
S <- matrix(0, dim(M))
Y <- matrix(0, dim(M))
while (!converged(M,L,S,tol)) {
L <- svd_shrink(M - S - (1/mu) * Y, mu)
S <- shrink(M - L + (1/mu) * Y, lamb * mu)
Y <- Y + mu * (M - L - S)
}
}
shrink <- function(X, tau) {
aX <- abs(X) - tau
sign(X) * pmax(aX,0)
}
svd_shrink <- function(X, tau) {
res <- svd(X)
res$u %*% (diag(shrink(res$d, tau)) %*% res$v)
}
converged <- function(M,L,S, tol) {
error = norm(M - L - S, "F") / norm(M, "F")
message("error =", error)
error <= tol
}
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