Replace NA values with the first value in all directions in R

I am looking to populate missing values in my table with non-NA value of the closest date, be it before or after the reference date. This means that a table like:

   date         value
03.03.2023        1
04.03.2023       NA
06.03.2023        4
09.03.2023       NA 
10.03.2023        3

Would be filled as:

   date         value
03.03.2023        1
04.03.2023        1
06.03.2023        4
09.03.2023        3 
11.03.2023        3

Explanation: Since 03.03. is closer to 04.03., locf is used. Yet since 11.03. is closer to 09.03., nocb (locf, fromLast = T) is used.

Eventual conflicts could take place if a NA value is flanked by two values of equal distance to the reference date. In this case, I would like locf to be preferred.

The code I have at the moment uses the stiff "locf" twice (once as standard and once as fromLast) and is not as flexible:

read.csv("path/to/merged_data.csv",
         colClasses = c("Date", "numeric", "numeric", "numeric", "character")) %>%
  group_by(field_id) %>%
  arrange(date) %>%
  mutate(
    Nearest_l8_locf = ifelse(!is.na(NDVI_l7) & is.na(NDVI_l8), na.locf(NDVI_l8), NDVI_l8),
    Nearest_s2_locf = ifelse(!is.na(NDVI_l7) & is.na(NDVI_s2), na.locf(NDVI_s2), NDVI_s2),
    Nearest_l8_locb = ifelse(!is.na(NDVI_l7) & is.na(NDVI_l8), na.locf(NDVI_l8, fromLast = TRUE), NDVI_l8),
    Nearest_s2_locb = ifelse(!is.na(NDVI_l7) & is.na(NDVI_s2), na.locf(NDVI_s2, fromLast = TRUE), NDVI_s2)
  ) %>%
  filter(!is.na(NDVI_l7)) %>%
  select(-NDVI_l8, -NDVI_s2) %>%
  relocate(field_id, .after = last_col()) %>%
  write_csv(file.path(results, "merged_data_interpolated.csv"))

In my actual case, the reference date are all dates for which a column (NDVI_l7) is not NA and the procedure to populate NA is done for two other columns (NDVI_l8 and NDVI_s2). It is also grouped by the column "field_id" since dates are repeated for each of those ID.

How can I adapt the code so that NA values are populated with the values of the closest date, regardless of where it is in the column?

I have managed to write a function for what I need.

# Function to find the nearest value to a given date

find_nearest_value <- function(x, target_date) {
  if (length(which(!is.na(x))) == 0) {
    return(NA)
  }
  idx <- max(which(!is.na(x) & !is.na(target_date) & target_date >= x))
  if (is.na(idx)) {
    idx <- min(which(!is.na(x) & !is.na(target_date) & target_date <= x))
  }
  return(x[idx])
}

# Apply function
read.csv("path/to/merged_data.csv",
         colClasses = c("Date", "numeric", "numeric", "numeric", "character")) %>%
  group_by(field_id, year = lubridate::year(date)) %>%
  arrange(date) %>%
  mutate(
    Nearest_l8 = ifelse(!is.na(NDVI_l7) & is.na(NDVI_l8), find_nearest_value(NDVI_l8, date), NDVI_l8),
    Nearest_s2 = ifelse(!is.na(NDVI_l7) & is.na(NDVI_s2), find_nearest_value(NDVI_s2, date), NDVI_s2),
  ) %>%
  ungroup() %>%
  filter(!is.na(NDVI_l7)) %>%
  select(-NDVI_l8, -NDVI_s2, -year) %>%
  relocate(field_id, .after = last_col()) %>%
  write_csv(file.path(results, "merged_data_function_year.csv"))

Note that I added an extra step to group by year in my code. This is because the resulting values weren't being normally distributed. My specific data is affected by seasonality and only pertains to the months of April through July. Restraining the operation of the function to a single year solved the problem.

another variant with base R only:

d being your example data:

d <- structure(list(date = structure(c(19419, 19420, 19422, 19425, 
19426), class = "Date"), value = c(1L, NA, 4L, NA, 3L)), row.names = c(NA, 
5L), class = "data.frame")

convert column date to class Date:

d$date <- as.Date(d$date, '%d.%m.%Y')

exploit the distance function to find closest neighbour:

impute_from_neighbours <- function(values, dates){
  dists <- dist(dates) |> as.matrix()
  dists[dists == 0] <- NA
  na_pos <- which(is.na(values))
  closest_non_na_pos <- apply(dists[, na_pos], 2, which.min)
  values[na_pos] <- values[closest_non_na_pos]
  values
}

d$value <- impute_from_neighbours(d$value, d$date)

output:

> d
        date value
1 2023-03-03     1
2 2023-03-04     1
3 2023-03-06     4
4 2023-03-09     3
5 2023-03-10     3