EzTao (易道)

EzTao is a toolkit for conducting AGN time-series/variability analysis, mainly utilizing the continuous-time auto-regressive moving average model (CARMA)

Installation

pip install git+https://github.com/ywx649999311/EzTao.git

Dependencies

python = ">=3.8,<3.12"
celerite = ">= 0.3.0"
scipy = "> 1.5.0"
numba = ">= 0.57.0"
matplotlib = ">=3.3.3"
emcee = ">=0.3.0"

Quick Examples

Let's first simulate a DRW/CARMA(1,0) process with a variance of 0.3^2 and a relaxation timescale of 100 days. This time series will have a total of 200 data points and span 10 years.

import numpy as np
import matplotlib.pyplot as plt
from eztao.carma import DRW_term
from eztao.ts import gpSimRand

# define a DRW kernel & and simulate a process
amp = 0.2
tau = 100
DRW_kernel = DRW_term(np.log(amp), np.log(tau))
t, y, yerr = gpSimRand(DRW_kernel, 10, 365*10, 200)

# now, plot it
fig, ax = plt.subplots(1,1, dpi=150, figsize=(8,3))
ax.errorbar(t, y, yerr, fmt='.')
...

We can fit the simulated time series to the DRW model and see how well we can recover the input parameters.

from eztao.ts import drw_fit

best_fit = drw_fit(t, y, yerr)
print(f'Best-fit DRW parameters: {best_fit}')

Best-fit DRW parameters: [0.17356983 88.36262467]

How does the power spectrum density (PSD) compare?

from eztao.carma import gp_psd

# get psd functions
true_psd = gp_psd(DRW_kernel)
best_psd = gp_psd(DRW_term(*np.log(best_fit)))

# plot
fig, ax = plt.subplots(1,1, dpi=150, figsize=(6,3))
freq = np.logspace(-5, 2)
ax.plot(freq, true_psd(freq), label='Input PSD')
ax.plot(freq, best_psd(freq), label='Best-fit PSD')
...

Note: How well the input and best-fit PSD match is up to how good the best-fit parameters are, which is highly influenced by the quality of the input time series.

For more examples, please check out the online documentation or run the tutorial notebooks at -> .

Development

poetry is used to solve dependencies and to build/publish this package. Below shows how setup the environment for development (assuming you already have poetry installed on your machine). Warning: poetry is having issue installing llvmlite = 0.34.0 (used for eztao = ^0.4.0) under Python 3.9. The issue disappears for Python 3.8.

1. Clone this repository, and enter the repository folder.
2. Create a python virtual environment and activate it (the virtual environment name must be '.venv').

   python -m venv .venv
   source .venv/bin/activate
   

3. Install dependencies and EzTao in editable mode.

   poetry install
   

Now you should be ready to start adding new features. Be sure to checkout the normal practice regarding how to use poetry on its website. When you are ready to push, also make sure the poetry.lock file is checked-in if any dependency has changed.

Citation

We are working on a paper to describe the full implementation of EzTao. In the meantime, if you find EzTao useful for your research, please consider acknowledging EzTao using the following:

@MISC{Yu2022,
       author = {{Yu}, Weixiang and {Richards}, Gordon T.},
        title = "{EzTao: Easier CARMA Modeling}",
     keywords = {Software},
 howpublished = {Astrophysics Source Code Library, record ascl:2201.001},
         year = 2022,
        month = jan,
          eid = {ascl:2201.001},
        pages = {ascl:2201.001},
archivePrefix = {ascl},
       eprint = {2201.001},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2022ascl.soft01001Y},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}