Halo clustering — `xi_hh`, `xi_hh_smallr`, `r_ab`¶

`xi_hh` — full-scale halo–halo correlation (derived)¶

ξ_hh(r | M₁, M₂) for differential mass-bin pairs, over the full xi_mm support. A derived property combining xi_mm, b_cum, xi_hh_smallr, and r_ab.

import numpy as np
res = reg.predict("xi_hh", "LCDM", 0.25, [0.31, 0.677, 0.967, 0.83])   # default 0.1-dex bins
res = reg.predict("xi_hh", "LCDM", 0.25, theta,
                  edges=np.array([13.0, 13.3, 13.6]),   # your bin edges (log10M)
                  r=np.geomspace(3, 90, 40),            # custom radii (optional)
                  route="auto")                         # auto | exact | bbar

res["xi_hh"]      # (Nbin, Nbin, Nr)
res["r"]          # radii (Mpc/h)
res["bin_edges"]  # the mass-bin edges used
res["b_bin"]      # per-bin <b>
res["validity"]   # per-gravity gate evidence — READ IT

Routes¶

exact (default via auto) — exact count-weighted mixed-difference, validated over r ∈ [2.2, 100] Mpc/h. Small-r pairs have NaN inside the halo-exclusion wedge — that is physics, not a bug.
bbar — pure factorization ⟨b⟩⟨b⟩ξ_mm, only good for r ∈ [20, 70] Mpc/h.

Limits¶

Bin edges above log₁₀M = 14 use the Tinker-extended b with D = 1.
Requested r outside the xi_mm support [2.04, 124.8] Mpc/h raises.

Accuracy: full-scale ξ_hh 1–2 % to 60 Mpc/h (ΛCDM), 2.0–2.6 % (f(R)); noise-floor-limited beyond.

`xi_hh_smallr` — small-r departure emulator (trained)¶

The trained threshold-level small-scale departure surface (the "D-surface") that xi_hh uses below the factorization window. The f(R) artifact carries a coefficient-scale-relative GP jitter floor (jitter_floor_frac = 0.05) that regularises under-fit high PCA modes — small-r ξ_hh reconstruction bands ≈ 6 % better. Not usually called directly.

`r_ab` — halo–matter cross-correlation coefficient (trained)¶

rab = reg.predict("r_ab", "LCDM", 0.25, [0.31, 0.677, 0.967, 0.83])   # (1, 30, 30)
art = reg.load("r_ab", "LCDM", 0.25)
art.thresholds   # both matrix axes (log10M thresholds)

Output: (1, 30, 30) threshold-pair matrix on the b_cum grid.
Used as a stochasticity / validity guard for b_diff and xi_hh.

Redshift¶

All three registered at z = 0.25 only.

Halo clustering — xi_hh, xi_hh_smallr, r_ab¶

xi_hh — full-scale halo–halo correlation (derived)¶