COVO

COVO stands for "Correlations of Vector Orientations" and is a C++ code for computing two-point correlations of 3D vector fields sampled at discrete particle positions.

Definitions

COVO computes two types of correlations:

$$\eta_{vv}(r) = \langle |{\bf \hat v}_{a} \cdot {\bf \hat v}_{b}|^{\gamma}\rangle (r) \ ,$$

and

$$\eta_{vr}(r) = \langle |{\bf \hat v}_{a} \cdot {\bf \hat r}_{ab}|^{\gamma}\rangle (r) \ ,$$

where v̂_a and v̂_b are normalized three-dimensional vectors at positions a and b, r̂_ab is the normalized distance vector pointing from position a to position b, and ⟨…⟩ denotes the average over all possible vector pairs separated by distance r = |r_ab|. The exponent γ is typically set to 1 or 2, resulting in η(r)=1/2 or η(r)=1/3 for randomly oriented vectors.

Features

• Both auto- and cross-correlations between two fields can be computed
• Two vectors are assigned to each position, allowing for the computation of multiple correlations in one run
• Operates in both cubical and spherical volumes
• Includes a simple spatial tree structure (using cubical grid cells or HEALPix cells for cubical or spherical volumes respectively) that serves two purposes:
  • Accelerated computation
  • Jackknife sampling for error estimation
• Parallel computation on shared memory using OpenMP

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Compilation

make -C src

The executable covo will be created in the project root directory.

Usage

Basic Usage

COVO searches for pairs of objects belonging to two different input catalogues. The catalogues can be specified in the parameter file or provided as command-line arguments.

Option 1: All parameters are specified by the parameter file

./covo covo.params

Option 2: Catalogue_1 is provided as input argument, catalogue_2 is copied from catalogue_1

./covo covo.params catalogue_1.csv

Option 3: Both catalogues are provided as input arguments

./covo covo.params catalogue_1.csv catalogue_2.csv

Option 4: Output file or suffix for output file as last argument (other options are set in parameter file)

./covo covo.params catalogue_1.csv catalogue_2.csv output_file.csv

Parameters

Parameters are set and described in covo.params. See the parameter file for detailed documentation of all available options.

File Format

Input files are CSV files containing information on the position and components of two vectors for each object:

x, y, z, vec_a_x, vec_a_y, vec_a_z, vec_b_x, vec_b_y, vec_b_z

Both input catalogues must have the same format. Column numbers and delimiters are configured in the parameter file.

Output files are CSV files with one row per distance bin. The output format (header presence, delimiter, column selection) can be configured via parameters in the parameter file (header_out, delim_out).

Regression Testing

Tools for regression testing are available to ensure code changes do not alter numerical results. See tests/README.md for details.

Run regression tests with:

make -C src test

Reference

If you use this code for your research, please provide a link to this repository when publishing the results.