# Summary

snr — **Figure.** Detection of a gravitational wave signal in noisy data. Top panel: Signal-to-noise ratio (SNR) as a function of GPS time, with the SNR threshold (orange dashed line) indicating the minimum required for confident detection. The sharp peak crossing the threshold marks a detectable GW event. Bottom panel: Detector strain data versus GPS time, showing the gravitational wave waveform template (pink) aligned with a signal embedded in background noise (black).

**`gwsnr`** is a high-performance Python package for efficient and accurate computation of the **optimal signal-to-noise ratio** ($\rho_{\rm opt}$) and **probability of detection** ($P_{\rm det}$) in gravitational-wave (GW) astrophysics. It is designed for large-scale simulations of compact binary mergers—such as **BBH**, **BNS**, and **BH–NS** systems—and for hierarchical Bayesian inference studies that require repeated SNR or $P_{\rm det}$ evaluations under selection effects. Traditional SNR calculations rely on noise-weighted inner products and are computationally intensive. `gwsnr` overcomes this bottleneck by combining **NumPy** vectorization, **JIT compilation** via [`Numba`](https://numba.pydata.org/), [`JAX`](https://github.com/google/jax), and [`MLX`](https://ml-explore.github.io/mlx/), along with **Python multiprocessing**. This combination enables massive acceleration on both CPUs and GPUs, achieving several orders-of-magnitude speed-up over conventional approaches. --- ### Key Capabilities - **Noise-Weighted Inner Product:** Provides accurate SNR computation for arbitrary frequency-domain waveforms, including precessing and higher-order harmonic models available in [`LALSuite`](https://lscsoft.docs.ligo.org/lalsuite/lalsimulation/). Accelerated using multiprocessing and JIT-compiled routines, with optional `JAX` backend integration via [`ripple`](https://github.com/tedwards2412/ripple). - **Partial-Scaling Interpolation:** Implements an interpolation-based approach for aligned-spin or non-spinning binaries. Precomputes partial-scaled SNRs on parameter grids, enabling rapid recovery of $\rho_{\rm opt}$ by simple rescaling—dramatically reducing computational cost. - **ANN-Based $P_{\rm det}$ Estimation:** Incorporates a trained Artificial Neural Network (ANN) built with `TensorFlow` and `scikit-learn`, capable of estimating detectability for precessing systems using reduced-dimensional input derived from partial-scaled SNRs. The model can be retrained for different detectors or astrophysical scenarios. - **Hybrid SNR Recalculation:** Combines the speed of interpolation or ANN-based estimates with the precision of the inner-product method. Signals near the detection threshold are automatically re-evaluated for higher accuracy. - **Statistical $P_{\rm det}$ Models:** Implements Gaussian and non-central $\chi$-based statistical models for observed SNRs across single or multi-detector networks. Supports user-defined detection thresholds and catalogue-based sensitivity functions. - **Horizon Distance ($D_{\rm hor}$):** Calculates the maximum distance at which a source is detectable above a given $\rho_{\rm opt,thr}$, using either analytical rescaling or numerical root-solving. Useful for sensitivity studies and detector reach estimations. - **Integration and Extensibility:** Provides a modular API to flexibly combine waveform models, detector noise PSDs, and configuration parameters—ideal for population synthesis, rate estimation, and hierarchical inference with selection effects. --- ### Applications `gwsnr` underpins simulations and analyses of **GW population statistics**, **rate estimation**, and **lensed versus unlensed event predictions**—as demonstrated in the [`ler`](https://ler.readthedocs.io/en/latest/) package. Its computational efficiency makes it particularly suited for **hierarchical Bayesian frameworks** that require rapid, repeated evaluation of $P_{\rm det}$ across large parameter spaces.