Interpolate between each row of a data.frame

Question

I am looking to resample and interpolate between each row of a data.frame in a fast way. I don't mind working with data.table or other data structures if necessary. Here is a reproducible example :

df <- data.frame(x = c(0, 2, 10),
                 y = c(10, 12, 0))

Desired output : a function f(df, n), where n is the number of interpolation values that would lead to :

df_int <- f(df, 1)

# That would produce :
# df_int <- data.frame(x = c(0, 1, 2, 6, 10),
#                      y = c(10, 11, 12, 6, 0))

df_int <- f(df, 3)

# That would produce :
# df_int <- data.frame(x = c(0, 0.5, 1, 1.5, 2, 4, 6, 8, 10),
#                      y = c(10, 10.5, 11, 11.5, 12, 9, 6, 3, 0))

Some solutions were proposed using approx but that doesn't work in my case.

Answer 1

Without consideration of speed

interpolate_vector <- function(x, n) {
  Reduce(function(x, tail_x) {
    c(head(x, -1), seq(tail(x, 1), tail_x[1], length.out = n + 2))
  }, init = x[1], x = tail(x, -1))
}

f <- function(df, n) {
  as.data.frame(lapply(df, interpolate_vector, n))
}

f(df, 1)

   x  y
1  0 10
2  1 11
3  2 12
4  6  6
5 10  0

f(df, 3)

     x    y
1  0.0 10.0
2  0.5 10.5
3  1.0 11.0
4  1.5 11.5
5  2.0 12.0
6  4.0  9.0
7  6.0  6.0
8  8.0  3.0
9 10.0  0.0

---

Without Reduce and growing vectors:

interpolate_vector_2 <- function(x, n) {
  res <- numeric(length = (length(x)-1) * (n+1) + 1)
  for (i in head(seq_along(x), -1)) {
    res[(i + (i-1)*n) : (i + i*n + 1)] <- 
      seq(x[i], x[i+1], length.out = n+2)
  }
  res
}

f_2 <- function(df, n) {
  as.data.frame(lapply(df, interpolate_vector_2, n))
}

---

Benchmark template (including @Maël's answers):

res <- bench::press(
  rows = c(1e2, 1e3),
  n = c(1, 3, 10),
  {
    df <- data.frame(
      x = runif(rows),
      y = runif(rows)
    )
    bench::mark(
      zoo = f_3(df, n),
      loop = f_2(df, n),
      reduce = f(df, n),
      approx = f_4(df, n)
    )
  }
)