When importing CSV into R how to generate column with name of the CSV?

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You have already done all the hard work. With a fairly small modification this should be straight-forward.

The logic is:

  1. Create a small helper function that reads an individual csv and adds a column with the file name.
  2. Call this helper function in llply()

The following should work:

read_csv_filename <- function(filename){
    ret <- read.csv(filename)
    ret$Source <- filename #EDIT
    ret
}

import.list <- ldply(filenames, read_csv_filename)

Note that I have proposed another small improvement to your code: read.csv() returns a data.frame – this means you can use ldply() rather than llply().

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