R: Conversion of the nested list to a data frame and obtaining list level names and other factors

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I have a nested list:

list1 <- list("A"=c(1,1,1), "B"=c(2,2,2), "C"=c(3,3,3))
list2 <- list("F1" = list1, "F2" = list1)

and I would like to get the last level of the list (containing the vector) as a dataframe and I would like to get the levels of the list as factors:

  Level1 Level2 V1 V2 V3
1     F1      A  1  1  1
2     F1      B  2  2  2
3     F1      C  3  3  3
4     F2      A  1  1  1
5     F2      B  2  2  2
6     F2      C  3  3  3

The first part is nicely given by:

data.frame(matrix(unlist(list2), ncol=3, byrow=T))

However, I did not find a nice way to also get the list-level-names as factors in the same dataframe. Any ideas? :)

Edit: The procedure should work up to p dimensions.


melt from "reshape2" has a method for lists. Perhaps it can be used in this case. Something like this:

library(reshape2)
dcast(cbind(
  coln = sequence(rapply(list2, length)),
  melt(list2)), L1 + L2 ~ coln,
  value.var = "value")
#   L1 L2 1 2 3
# 1 F1  A 1 1 1
# 2 F1  B 2 2 2
# 3 F1  C 3 3 3
# 4 F2  A 1 1 1
# 5 F2  B 2 2 2
# 6 F2  C 3 3 3