Created
November 25, 2022 08:29
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In R: Draw sample from a grid without creating it (without replacement)
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| library(microbenchmark) | |
| library(Rcpp) | |
| library(inline) | |
| src <- "int n = as<int>(N); | |
| std::vector<int> s = as< std::vector<int> >(sizes); | |
| std::vector<int> epsilon (s.size()); | |
| std::vector<int>::iterator it; | |
| it = s.begin(); | |
| it = s.insert ( it , 1 ); | |
| int G[s.size()]; | |
| std::partial_sum (s.begin(), s.end(), G, std::multiplies<int>()); | |
| int k; | |
| while(n>0){ | |
| k=1; | |
| while(G[k]<=n){ | |
| k=k+1; | |
| } | |
| epsilon[k-1] = (int)n / G[k-1]; | |
| n = n % G[k-1]; | |
| } | |
| return wrap(epsilon); " | |
| intToCantor <- cxxfunction(signature( | |
| N = "integer", | |
| sizes = "integer" | |
| ), | |
| body = src, plugin = "Rcpp" | |
| ) | |
| CantorToInt <- function(epsilon, sizes) { | |
| sum(epsilon * c(1, cumprod(sizes[1:(length(epsilon) - 1)]))) | |
| } | |
| x <- 1:1000 | |
| y <- 1:1000 | |
| z <- 1:1000 | |
| sizes <- c(length(x), length(y), length(z)) | |
| N <- prod(sizes) | |
| n <- 10000 | |
| idx <- sample(1:N, n, replace = FALSE) | |
| result <- matrix(NA_real_, nrow = n, ncol = length(sizes)) | |
| for (i in 1:n) { | |
| indices <- 1 + intToCantor(idx[i] - 1, sizes = sizes) | |
| result[i, ] <- c(x[indices[1]], y[indices[2]], z[indices[3]]) | |
| } | |
| X <- list(x, y, z) | |
| microbenchmark(A = { | |
| for (i in 1:n) { | |
| indices <- 1 + intToCantor(idx[i] - 1, sizes = sizes) | |
| result[i, ] <- c(x[indices[1]], y[indices[2]], z[indices[3]]) | |
| } | |
| }, B = { | |
| X.len <- sapply(X, length) | |
| # modify '%%' to return values 1..n instead of 0..(n-1) | |
| mod2 <- function(x, y) (x - 1) %% y + 1 | |
| result <- sapply(seq_along(X), function(i) { | |
| X[[i]][mod2( | |
| ceiling(idx / prod(X.len[seq_len(i - 1)])), | |
| X.len[i] | |
| )] | |
| }) | |
| }) |
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