Whenever I want to do something "map"py in R, I usually try to use a function in the apply family.

However, I've never quite understood the differences between them -- how {sapply, lapply, etc.} apply the function to the input/grouped input, what the output will look like, or even what the input can be -- so I often just go through them all until I get what I want.

Can someone explain how to use which one when?

My current (probably incorrect/incomplete) understanding is...

1. sapply(vec, f): input is a vector. output is a vector/matrix, where element i is f(vec[i]), giving you a matrix if f has a multi-element output

2. lapply(vec, f): same as sapply, but output is a list?

3. apply(matrix, 1/2, f): input is a matrix. output is a vector, where element i is f(row/col i of the matrix)
4. tapply(vector, grouping, f): output is a matrix/array, where an element in the matrix/array is the value of f at a grouping g of the vector, and g gets pushed to the row/col names
5. by(dataframe, grouping, f): let g be a grouping. apply f to each column of the group/dataframe. pretty print the grouping and the value of f at each column.
6. aggregate(matrix, grouping, f): similar to by, but instead of pretty printing the output, aggregate sticks everything into a dataframe.

Side question: I still haven't learned plyr or reshape -- would plyr or reshape replace all of these entirely?