What is a delta vector/partial sum vector?
Given an integer vector a with length n, its partial sum vector is another integer vector b with length n + 1, with values defined as:
b(0) = initial sum
b(i ) = a(0) + a(1) + ... + a(i - 1) i = 1, 2, ..., n
Given an integer vector with length n + 1, its delta vector is another integer vector b with length n, with values defined as:
b(i ) = a(i ) - a(i - 1), i = 0, 1, ... , n -1
In this issue, we provide utilities to convert between vector and partial sum vector. It is interesting to note that the two operations corresponding to the discrete integration and differentian.
These conversions have wide applications. For example,
1. The run-length vector proposed by Micah is based on the partial sum vector, while the deduplication functionality is based on delta vector. This issue provides conversions between them.
2. The current VarCharVector/VarBinaryVector implementations are based on partial sum vector. We can transform them to delta vectors before IPC, to reduce network traffic.
3. Converting to delta can be considered as a way for data compression. To further reduce the data volume, the operation can be applied more than once, to further reduce data volume.