Find the minimum value that data could have had before it was rounded

Question

I have this function in R:

Minimum <- function(data) {
    answer <- numeric(length(data))

    diference <- c(0, diff(data, lag = 1, differences = 1)) #Padded initially =0

    answer[1]=data[1]
    for (i in 2:length(diference)) {
        if (diference[i]==0) {
            answer[i]=answer[i-1]
        } else {
            answer[i]=data[i]-diference[i]/2
        }
    }
    return(answer)
}

Its purpose is to find the minimum value which "data" could had before it was rounded.

The minimum possible value is the average of the values which "data" had at the last change of value in "data"

This code works, but since for loops are inefficient in R, it is advised to vectorize the function.

The problem is that the "answer" vector depends on the former values in "answer", so I cannot use a lambda function.

Answer 1

You can firstly change by difference != 0 and then use na.locf to replace NAs by last available value recursively.

minimum_new <- function(data) {
  answer <- rep(NA, length(data))
  difference <- c(0, diff(data, lag = 1, differences = 1)) / 2
  answer[1] <- data[1]
  answer[difference != 0] <- data[difference != 0] - difference[difference != 0]
  answer <- zoo::na.locf(answer, na.rm = FALSE)
  answer
}

This version is faster for me by at least 2 times.

> data <- sample(10, 10000, replace = TRUE)
> check <- function(values) all(sapply(values[-1], function(x) identical(values[[1]], x)))
> bench <- microbenchmark::microbenchmark(loop = Minimum(data), vectorised = minimum_new(data), check=check)
Unit: microseconds
       expr      min       lq     mean   median       uq      max neval cld
       loop 1401.959 1415.552 1665.816 1457.274 1586.407 4620.835   100   b
 vectorised  742.325  758.183 1111.202  796.507 1383.268 2587.940   100  a 

With check it's also checks the equality of output.