Performance

Plots in this section are generated by

uv run benchmarks performance-plot

Speed comparison

We benchmark the wall-clock time for decomposing all 4200 spectra in the GRS test field (424 channels each) using both PHSpectra and GaussPy+ (Riener et al. 2019). Each spectrum is processed individually through the full pipeline of each tool to ensure a fair per-spectrum comparison. Both algorithms are run with their recommended configurations:

• PHSpectra: $\beta = 3.5$ (default), C-accelerated Levenberg-Marquardt solver and persistence peak detection
• GaussPy+: two-phase decomposition with $\alpha_1 = 2.89$, $\alpha_2 = 6.65$ (trained values from Riener et al. 2019, Sect. 4.1), SNR threshold = 3.0

Results

Metric	PHSpectra	GaussPy+	Factor
Total time (4200 spectra)	746.4 s	1477.4 s	2.0×
Mean per spectrum	177.7 ms	350.5 ms	2.0×
Median per spectrum	51.6 ms	40.4 ms	—
P95 per spectrum	705.4 ms	702.5 ms	—
P99 per spectrum	2976.0 ms	8407.5 ms	2.8×
Mean components detected	2.48	2.44	—

PHSpectra is 2× faster in total wall-clock time than GaussPy+. The median per-spectrum times are comparable (51.6 ms vs 40.4 ms), but the distributions have very different tails: GaussPy+'s P99 reaches 8.4 s compared to PHSpectra's 3.0 s, and these extreme outliers dominate the aggregate timing.

Figure 1. Performance benchmark for PHSpectra (solid) and GaussPy+ (dashed) on all 4200 GRS test-field spectra. Generated by uv run benchmarks performance-plot.

Timing characteristics

The two tools have similar median performance but differ sharply in tail behaviour:

• PHSpectra uses a custom C extension for both the bounded Levenberg-Marquardt solver (with analytic Jacobian) and persistence-based peak detection, keeping per-call overhead low. The timing distribution is tighter, with P99 at 3.0 s.

• GaussPy+ has comparable median performance but much higher variance (std dev 2013.8 ms vs 688.9 ms). A small fraction of spectra trigger long optimisation chains, with P99 reaching 8.4 s. These outliers dominate the mean and total time.

Algorithmic differences

1. No smoothing sweep. GaussPy+ convolves the spectrum with a family of Gaussian kernels at each $\alpha$ scale, computing derivatives at every scale. The two-phase decomposition repeats this process twice (once per $\alpha$). PHSpectra skips smoothing entirely — it operates directly on the raw spectrum using persistence-based peak detection, which is $O(n)$ in the number of channels.

2. No training required. GaussPy+'s $\alpha$ parameters must be trained per survey (or per survey region), which adds a separate computational cost not reflected in the per-spectrum timing. PHSpectra's $\beta$ parameter requires no training — the default value works across surveys.

3. Tail behaviour. PHSpectra's execution time is more predictable (P99 3.0 s vs 8.4 s). GaussPy+'s derivative-based approach can trigger costly iterative refinement on complex spectra, leading to extreme outliers that dominate aggregate timing.

Benchmark details

• Hardware: single-core sequential processing for both tools (no parallelization)
• PHSpectra: native Python 3.14, C extension for LM solver and peak detection
• GaussPy+: Python 3.10 in Docker (required for compatibility with legacy numpy/scipy); each spectrum is processed individually through the full GaussPyDecompose pipeline (init, decompose, improve_fitting, save)
• Spectra: all 4200 GRS test-field pixels, 424 velocity channels each