pyZDCF is a Python module that emulates a widely used Fortran program called ZDCF (Z-transformed Discrete Correlation Function, Alexander 1997). It is used for robust estimation of cross-correlation function of sparse and unevenly sampled astronomical time-series. This Python implementation also introduces sparse matrices in order to significantly reduce RAM usage when running the code on large time-series (> 3000 points).

pyZDCF is based on the original Fortran code fully developed by Prof. Tal Alexander from Weizmann Institute of Science, Israel (see Acknowledgements and References for details and further reading).

Full docs with examples: pyzdcf.readthedocs.io

Development of pyZDCF module was motivated by the long and successful usage of the original ZDCF Fortran code in the analysis of light curves of active galactic nuclei by our research group (see Kovacevic et al. 2014, Shapovalova et al. 2019, and reference therein). One of the science cases we investigate is photometric reverberation mapping in the context of Legacy Survey of Space and Time (LSST) survey strategies (see Jankov et al. 2022). However, this module is general and is meant to be used for cross-correlation of spectroscopic or photometric light curves, same as the original Fortran version.

pyZDCF can be installed using pip:

pip install pyzdcf

python = ">=3.8,<3.12"
numpy = ">=1.16.5"
pandas = "^1.3"
scipy = "^1.7.3"

This code requires user-provided plain text files as input. CSV files are accepted by default, but you can use any other delimited file, as long as you provide the sep keyword argument when calling pyzdcf function. The input light curve file should be in 3 columns: time (ordered), flux/magnitude and absolute error on flux/magnitude. Make sure to exclude the header (column names) from the input files.

First few lines of the example input file accepted by default (CSV):

0.0,0.9594479339474323,0.0019188958678948648
1.0,0.9588196871078336,0.0019176393742156672
2.0,0.9637198686651904,0.0019274397373303808
3.0,0.9622807967282166,0.0019245615934564328

NOTE: pyZDCF is tested only with input files having whole numbers (integers) for time column. If you have decimal numbers (e.g., you have a light curve with several measurments in the same night expressed as fractions of a day instead of minutes), just convert them into a time format with integer values (e.g., minutes instead of days). On the other hand, you could round the values from the same day (e.g. 5.6 --> 5, 5.8 --> 5, etc.) and the algorithm will take in the information and average the flux for that day.

If you use interactive mode (intr = True), then pyZDCF will ask you to enter all input parametars interactively, similarly to original ZDCF interface. There is also a manual mode (intr = False) where you can provide input parameters using a dictionary and passing it to parameters keyword argument.

Available input parameters (keys in the parameters dictionary) are:

• autocf - if True, perform auto-correlation, otherwise do the cross-correlation.
• prefix - provide a name for the output file.
• uniform_sampling - if True, set flag to perform uniform sampling of the light curve.
• omit_zero_lags - if True, omit zero lag points.
• minpts - minimal number of points per bin.
• num_MC - number of Monte Carlo simulations for error estimation.
• lc1_name - Name of the first light curve file
• lc2_name - Name of the second light curve file (required only if we do cross-correlation)

For more information on the correct syntax, see "Running the code" subsection.

The return value of the pyzdcf function is a pandas.DataFrame object displaying the results in 7 columns:

+---+-------+-------------+-------------+--------------+-------------+-------------+------+
|   |   tau |   -sig(tau) |   +sig(tau) |          dcf |   -err(dcf) |   +err(dcf) | #bin |
|---+-------+-------------+-------------+--------------+-------------+-------------+------|
| 0 |  -991 |           4 |           0 |  0.13598     |  0.361559   |  0.342224   |   10 |
| 1 |  -988 |           2 |           0 | -0.217733    |  0.279988   |  0.301034   |   13 |
| 2 |  -985 |           2 |           0 | -0.0614938   |  0.266546   |  0.27135    |   16 |
| 3 |  -982 |           2 |           0 |  0.239601    |  0.237615   |  0.223317   |   19 |
| 4 |  -979 |           2 |           0 |  0.331415    |  0.208171   |  0.192523   |   22 |

The columns are: time-lag, negative time-lag std, positive time-lag std, zdcf, negative zdcf sampling error, positive zdcf sampling error, number of points per bin. For more information on how these values are calculated see Alexander 1997.

The code will also generate an output .dcf file file in a specified folder on your computer with same 7 columns containing the results. It is allowed to name these files however you want using the prefix parameter (see example in the next subsection).

Optionally, by adding keyword argument savelc = True, pyzdcf can create and save light curve files used as input after averaging points with identical times.

An example for calculating cross-correlation between two light curves:

from pyzdcf import pyzdcf

input = './input/'           # Path to the input data
output = './output/'         # Path to the directory for saving the results

# Light curve names
lc1 = 'lc_name1'
lc2 = 'lc_name2'

# Parameters are passed to the pyZDCF as a dictionary

params = dict(autocf            =  False, # Autocorrelation (T) or cross-correlation (F)
              prefix            = 'ccf',  # Output files prefix
              uniform_sampling  =  False, # Uniform sampling?
              omit_zero_lags    =  True,  # Omit zero lag points?
              minpts            =  0,     # Min. num. of points per bin (0 is a flag for default value of 11)
              num_MC            =  100,   # Num. of Monte Carlo simulations for error estimation
              lc1_name          =  lc1,   # Name of the first light curve file
              lc2_name          =  lc2    # Name of the second light curve file (required only if we do CCF)
             )

# Here we use non-interactive mode (intr=False)
dcf_df = pyzdcf(input_dir  = input, 
                output_dir = output, 
                intr       = False, 
                parameters = params, 
                sep        = ',', 
                sparse     = 'auto', 
                verbose    = True)

# To run the program in interactive mode (like the original Fortran code):
dcf_df = pyzdcf(input_dir  = input, 
                output_dir = output, 
                intr       = True, 
                sep        = ',', 
                sparse     = 'auto', 
                verbose    = True
                )

• For more examples see example notebook.

• Additionally, you can also check out code description of the original Fortran version because the majority of input parameters and all output files are the same as in pyZDCF. You can download the fortran source code here.

• Sparse matrix implementation for reduced RAM usage when working with long light curves (>3000 points);

The main benefit is that we can now run these demanding calculations on our own personal computers (8 GB of RAM is enough for light curves containing up to 15000 points), making the usage of this algorithm more convinient than ever.

You can turn this on/off by specifying sparse keyword argument to True or False. Default value is 'auto', where sparse marices are utilized when there are more than 3000 points per light curve. Note that by reducing RAM usage, we pay in increased program running time.

• Interactive mode: program specifically asks the user to provide necessary parameters (similar to original Fortran version);
• Manual mode: user can provide all parameters in one dictionary.
• Fixed bugs from original ZDCF (v2.3) written in Fortran 95.

The module was tested (i.e., compared with original ZDCF v2.3 output, with fixed bugs) for various parameter combinations on a set of 100 AGN light curve candidates (g and r bands). The list of object ids and coordinates was taken from a combined catalogue of known AGNs (Sánchez-Sáez et al. 2021).

Distributed under the MIT License.

Isidora Jankov (main) - [email protected]
Andjelka Kovačević - [email protected]
Dragana Ilić - [email protected]

You are welcome to write to us:

• if there are any problems running the code on your system;
• suggestions for code improvements.

If you want to report a bug, please open an Issue on GitHub: https://github.com/LSST-sersag/pyzdcf.

If you use pyZDCF for scientific work leading to a publication, please consider acknowledging it using the following citation (BibTeX):

@software{jankov_isidora_2022_7253034,
  author       = {Jankov, Isidora and
                  Kovačević, Andjelka B. and
                  Ilić, Dragana and
                  Sánchez-Sáez, Paula and
                  Nikutta, Robert},
  title        = {pyZDCF: Initial Release},
  month        = oct,
  year         = 2022,
  publisher    = {Zenodo},
  version      = {v1.0.0},
  doi          = {10.5281/zenodo.7253034},
  url          = {https://doi.org/10.5281/zenodo.7253034}
}

For other citation formats see: https://doi.org/10.5281/zenodo.7253034

• The pyZDCF module is based on the original Fortran code developed by Prof. Tal Alexander (Weizmann Institute of Science, Israel). Download Fortran version from professor's page.
• For theoretical details regarding the ZDCF algorithm see this publication: Alexander, T. (1997).
• Huge thanks to my closest collegues and mentors Dr. Andjelka Kovačević and Dr. Dragana Ilić, as well as to Dr. Paula Sánchez-Sáez and Dr. Robert Nikutta for invaluable input during the development and testing of this python module.
• Many thanks to Prof. Eli Waxman, Amir Bar On and former students of Prof. Tal Alexander for their kind assistance regarding the development of pyZDCF module and its acknowledgment as part of the legacy behind late Prof. Alexander.

• Alexander, T. 1997, in: Astronomical Time Series, eds. D. Maoz, A. Sternberg, & E. M. Leibowitz, Vol. 218, Springer, Is AGN Variability Correlated with Other AGN Properties? ZDCF Analysis of Small Samples of Sparse Light Curves
• Jankov, I.; Kovačević A. B.; Ilić, D.; et al. 2022, Astronomische Nachrichten, 343, e210090
• Kovačević, A.; Popović, L. Č.; Shapovalova, A. I.; et al. 2014, Advances in Space Research, 54, 1414-1428
• Sánchez-Sáez, P.; Lira, H.; Martí, L.; et al. 2021,The Astronomical Journal, 162, id.206
• Shapovalova, A. I.; Popović, L. Č.; Afanasiev, V. L.; et al. 2019, MNRAS, 485, 4790-4803