OriginalIndex

OriginalIndex is a data concept used to record the original positions of elements before a transformation such as sorting, filtering, or grouping. It serves as a permutation vector that allows a program to map results back to the source order or to trace how the transformed data relates to its input.

Construction and interpretation are straightforward. To create an OriginalIndex, pair each element with its original index, sort by the element values (or by a chosen key), and extract the sequence of original indices in the resulting order. This sequence is the OriginalIndex. In many contexts, a related operation called argsort produces the indices that would sort the data, which effectively provides the OriginalIndex.

A simple example: given values [50, 20, 30], sorting ascending yields [20, 30, 50], and the OriginalIndex is [1, 2, 0], indicating that the first place in the sorted order comes from position 1, the second from 2, and the third from 0 in the original array. The OriginalIndex is used to reconstruct the original arrangement after processing or to apply results back to the initial data order.

Variants and properties include treating the OriginalIndex as a permutation vector of length n, with memory overhead proportional to the input size. Handling duplicate keys may require deterministic tie-breaking rules. Applications span data analysis, database query processing, graphics and visualization pipelines, and any scenario where transformed results must be mapped to or traced back to the original data sequence. See also permutation, inverse permutation, and index mappings.