kdcount is a simple API for brute force pair counting, there is a C interface and a Python interface. It uses a KDTree to prune the K-D spatial data; for each pair within a given distance D, a callback function is called; the user-defined callback function does the actual counting.
To cite kdcount, use the DOI via Zenodo
Periodic boundary is supported, and it is non-trivial.
The python interface is more complicated, and powerful:
The calculation can be made parallel, if :py:mod:`sharedmem` is installed.
easy_install --user sharedmem
Refer to the to the API Reference at http://rainwoodman.github.io/kdcount
The time complexity is
O[(D / n) ** d],
where n is number density. Each pair is opened.
Note that smarter algorithms exist (more or less, O(D / n log Dn), I may remembered it wrongly See Gary and Moore 2001. The smarter algorithm is internally implemented, but not very much tested, and undocumented; do not use it.
Unfortunately in cosmology we usually want to project the pair separation along parallel + perpendicular direction relative to a given observer -- in this case, the smarter algorithm become very difficult to implement.
The spatial complexity is a constant, as we make extensive use of callback functions