This archive contains a basic version of the code used in
  M. Kerscher, A&A 666 (2022) A181
  https://doi.org/10.1051/0004-6361/202243632
  https://arxiv.org/abs/2203.13288
It implements the standard, the exact, and an improved version of the
Landy & Szalay estimator.

* As prerequisites you need
  - a Python environment with numpy and scipy (> 1.7.0), for example Anaconda
    https://docs.anaconda.com/anaconda/install/index.html
  - pybind11, which is used to interface the C++ code from within python
    https://pybind11.readthedocs.io/en/stable/installing.html
  - a C++ compiler which supports OpenMP; g++ under Linux works.
    On MacOS I suggest you disable OpenMP in the Makefile (in principle
    it should be possible to use OpenMP on MacOS, but I did not have
    enough pertinacity).

* As soon as pybind11 is installed, typing
    make
  should create the shared libarary from cppauxiliary.cpp such that
  the parallelized C++ functions can be called from python. For
  details see the Makefile and pyauxiliary.py. 

* In pyauxiliary.py you find the code implementing the standard
  Landy & Szalay estimator using the pair-counts DD, DR, and RR, as
  well as the exact estimator and the estimator using quasi Monte
  Carlo. There we call the functions from the shared library.

* The code for the area fraction is in baddeley.py .
  If you use baddeley.py please give credit to
    A.J. Baddeley, R.A. Moyeed, C.V.Howard, A.Boyde,
    Appl. Statist., 42, 641 (1993).
  The implementation in baddeley.py follows closely the C-code in
  sphefrac.c from the R package spatstat (written by A.J. Baddeley).
  Errors in the python implementation should be blamed on me.

* A simple example using the different estimators is given in
  xi.py. It reads the point set from "points.pt", calculates the
  different estimates of the two-point correlation function, and
  then prints and plots them (compare cxi.pdf and cxilog.pdf).

* On a small desktop machine (from 2018) this calculation took
  less than 2 min. In the example xi.py, the numerical integration
  for the exact result requires most of the time. This changes
  quickly if you increase the number of points. And clearly the
  number of points should be increased for serious work.

If you find my code helpful it would be nice if you could cite the
article mentioned on top this file.

All the best
Martin Kerscher
Munich, October 2022