We often need to "reindex" one array/vec/series/frame so as to produce a new one.

First, note that an array A of values of type T is actually a mapping defined as

              f
[0, A.length) => {T}

That is, each integer index of the array yields a value of type T when it is de-referenced.

ReIndexer has two fields, lTake and rTake, which are array-based maps defined for some integers M and N as

        g
[0, N) => [-1, M)

In other words, lTake and rTake are arrays of length N whose entries are integers between -1 and M-1. We call these "indexers".

Given a reindexer, g, a re-indexing operation on array A yields a new array B of length N which represents the following mapping:

        B
[0, N)  =>  {T}

where B(i) == f(g(i)) if g(i) != -1
            == NA      if g(i) == -1

For this to work, the maximum value M in the co-domain of g must be <= A.length. We also augment the mapping f to send -1 to the corresponding NA value of type T.

For example, suppose we have Index(0,1,2,4) and Index(0,1,2,3). Performing a full outer join would yield the following ReIndexer:

• lTake = {0, 1, 2, -1, 3},
• rTake = {0, 1, 2, 3, -1},
• index = Index(0, 1, 2, 3, 4).

These indexers are then amenable to using with org.saddle.array.take to select elements out of an indexed data structure.

A performance optimization is to make lTake and rTake of type Option[Array], where we make a value of None behave as if it were an array of [0, N). So, the "taking" code knows to take the original values. You will therefore see code that looks like:

val v = Vec(...)
val ixer = ReIndexer(...)
ixer.lTake.map(x => v.take(x)) getOrElse v