Triangle-GB

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Frequency-domain GB TDI-2.0 response, as an example for the analysis of Taiji Data Challenge.

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# Triangle-GB
This repository provides examples for the fast time-delay interferometry (TDI) response model of Galactic binaries (GBs), along with tutorials for some simple data analysis tasks based on **Taiji Data Challenge II** and **LISA Data Challenge**. The response model is inspired by the "TDI on the fly" approach proposed in [N. J. Cornish et al, PRD (2025)](https://doi.org/10.1103/y718-c1xl), and has been reformulated to support arbitrary detector orbit and arbitrary TDI combination. 
Our implementation of the fast response model has been validated against the more precise (but slower) time-domain simulation implemented in ``Triangle-Simulator``, with residuals well below the instrumental noise level.

# Installation 
Please ensure ``Triangle-Simulator`` is available in your Python environment, which provides essential constants, utilities, and response functions, and you may also need to install ``bilby`` for some examples.

1. **Install Triangle-Simulator**    
   install [Triangle-Simulator](https://github.com/TriangleDataCenter/Triangle-Simulator) and activate the tri_env environment by
   ```sh 
   conda activate tri_env 
   ```

2. **Install Nested Sampling Tools for some Examples**
   ```sh
   pip install bilby nessai-bilby
   ```

# What's in the examples 
- Waveform modeling in both time and frequency domains; 
- Rapid search of GB signals using $\mathcal{F}$-statistics and maximum likelihood estimation; 
- Posterior inference of GB signals with nested sampling; 
- Application on both **Taiji Data Challenge II** and **LISA Data Challenge**.

# References 
- [The TDC II paper](https://arxiv.org/abs/2505.16500). 
- [The fast GB response model for arbitray orbit and TDI (in preparation)](???)

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