Reproducing the paper¶

All commands run from paper/ with the [pe] extra installed. The cached posterior chains ship in paper/results/, so every chain-based figure regenerates in minutes — without lisabeta and without sampling. lisabeta and the from-scratch runs are needed only to regenerate the chains themselves.

Figures from the cached chains¶

cd paper

python make_figures.py        # corner_key_{A,B}, corner_noise_{A,B},
                              # corner_fullkey_{A,B}, upsilon_xi(.png/_heatmap),
                              # overview                            (~10 min)
python plot_scenC.py          # corner_key_C_full_diag_td, corner_noise_C_...,
                              # cov_colormap_C
python plot_ABC.py            # corner_key_full_ABC
python fig_cov_colormap.py    # cov_colormap_ABC

The scaling figure¶

Depends on gaplike alone — no lisabeta, no chains. It times a single quadratic form \(\mathbf{n}_O^{T}\Sigma_{OO}^{-1}\mathbf{n}_O\) as the record length grows, comparing the dense route against matrix-free preconditioned conjugate gradients. The dense route is deliberately given nothing to exploit — no simultaneous diagonalization, no two-component spectrum — so that it stands for the general case.

python fig_cg_scaling.py      # -> results/cg_scaling.json   (~15-30 min)
python _mkfig.py              # -> figures/cg_scaling.{png,pdf}

--kmax-cg and --kmax-dense shorten the sweep. results/cg_scaling.json ships with reference timings (two cores of an Intel Xeon at 2.80 GHz), so _mkfig.py works out of the box.

The preconditioner comparison¶

Also gaplike alone. Circulant (Whittle) against the sparse tapered autocovariance of Baghi et al. (2016), as a fixed amount of missing time is chopped into 1 … 256 gaps: iteration count and cost per likelihood call. See Which preconditioner for what the two curves mean.

python fig_precond_compare.py   # -> results/precond_compare.json  (~4 min)
python fig_precond_compare.py --plot        # redraw from the cache

Linearised vs Godambe–White¶

Noise sector only — no lisabeta, no chains. Computes \(\Upsilon\) both ways for the four covariance models over 57 gap patterns at fixed missing time, which is how Υ and Ξ states the criterion for when the linearised formalism suffices.

python fig_upsilon_formalisms.py            # -> results/  (~8 min)
python fig_upsilon_formalisms.py --plot     # redraw from the cache

The determinant benchmark¶

Beyond the paper: the same comparison for the likelihood’s other half, \(\log\lvert\Sigma_{OO}\rvert\) — dense Cholesky against the exact complement identity and matrix-free SLQ (Determinants), plus the shared-probe difference experiments under ratio-spline perturbations. Also gaplike-only.

python fig_det_scaling.py --kmax-slq 14 --kmax-dense 14 --kmax-comp 15
python fig_det_flexible.py    # -> results/det_flexible*.json
python mkfig_det.py           # -> figures/det_scaling.{png,pdf}

Regenerating the chains¶

Needs lisabeta and hours of sampling.

python driver.py              # A/B x {full,diag,bare,psd}    (~80 min, 2 cores)
python scenC_run.py           # C: FD full + convolved diagonal + exact TD PE
python ensemble_noise.py      # 300-realization ensemble: pseudo-true points,
                              # sandwich scatter

The scenarios¶

	pattern	duty	SNR
A	two long gaps, 1 h each, 0.3 h Planck tapers	—	585
B	twelve short gaps, 9 min hourly, 0.05 h tapers	—	743
C	drastic comb, 150 s removed every 750 s, rectangular	80%	319

The no-gap reference is SNR 902. Scenario C is where the approximation hierarchy breaks: the convolved diagonal stays accurate but its widths are an order of magnitude wider than the data allow, and one of the two exact treatments becomes necessary.

Notebooks¶

Two worked examples ship in notebooks/.

exact_inference_demo.ipynb runs end to end without lisabeta: gapped two-channel LISA noise plus a toy chirp, a joint four-parameter PE with both TimeDomainExact and FullCovariance, and a comparison corner showing the two posteriors on top of each other.

mbhb_gaps_demo.ipynb injects an MBHB with parameters of your choosing, compares five gap configurations by duty cycle and recoverable SNR, and sets up a complete joint thirteen-parameter inference — likelihood, priors, walkers, sampler — ready but not launched.

anim_leakage.py renders the animation used in talks: four acts taking a raw record through record-edge tapering, sharp-edged gaps and tapered gaps, with the spectral kernel, the modelled PSD and the bin-to-bin correlation matrix side by side.

anim_upsilon_xi.py renders the two Υ/Ξ talk animations (The Υ and Ξ diagnostics embeds and explains both) into assets/: upsilon_xi_quadrants.gif — four analyses as repeated experiments, one per quadrant of the (Υ, Ξ) plane, every case anchored to the paper’s measured values — and upsilon_xi_pp.gif — the same four analyses through a PP plot, which measures Υ and only Υ. The anchor values are regenerated by paper/dump_upsxi.py (needs lisabeta); the animations themselves need nothing beyond numpy/scipy/matplotlib. The companion interactive explorer, assets/upsilon_xi_explorer.html, opens in any browser: sliders for Υ and Ξ (stopping at the information bound Υ·Ξ ≥ 1), the paper anchors click-to-load, and live interval and PP views.