Per-galaxy contributions

MeasureIABox.measure_galaxy_contributions resolves the box alignment estimator per shape galaxy: one pair traversal returns, for every shape galaxy \(j\) and radial bin \(b\), its contribution \(Y_j(b)\) to the signal and the number of pairs \(P_j(b)\) it contributed through, such that

is exactly the ordinary estimator. \(Y_j(b)/P_j(b)\) is then the mean alignment contribution of that galaxy in that bin.

This is the input needed to regress the alignment signal on per-galaxy properties. A per-bin least-squares fit of the pair contributions on standardised galaxy properties has normal equations

so any number of properties can be fitted from a single pair traversal, instead of one correlation-function run per weighting. It is available for the box only.

Running it

from measureia import MeasureIABox

mi = MeasureIABox(data_dict, output_file_name="./out.hdf5", boxsize=205.0)

out = mi.measure_galaxy_contributions(
    "ds1",
    num_jk=27,              # optional: also decompose by jackknife patch
    statistic="multipoles",  # or "w" for w_g+(r_p)
    ell=2,                   # multipole order (spin taken equal to it)
    temp_file_path=False,    # a path is required when num_nodes > 1
    return_output=True,      # omit to write to the output file instead
)

out["Y"].sum(axis=0)   # == the ordinary xi_g+,2(r) from measure_xi_multipoles
out["Y"] / out["P"]    # mean contribution per galaxy per bin

statistic="multipoles" projects onto \(\tilde\xi_{g+,\ell}(r)\) in \((r, \mu_r)\) bins, statistic="w" onto \(w_{g+}(r_p)\) in \((r_p, \Pi)\) bins. The ellipticity, responsivity, masks and rp_cut arguments behave exactly as in measure_xi_multipoles, so the per-galaxy decomposition matches the correlation function you would otherwise measure. With num_nodes > 1 the traversal runs on multiple cores and needs temp_file_path plus the usual if __name__ == "__main__": guard.

Jackknife realisations without re-counting pairs

With num_jk > 0, both \(Y\) and \(P\) are additionally decomposed by the jackknife sub-box of the position-sample partner. That is enough to rebuild every delete-one realisation from the single traversal — dropping the shape galaxies in the omitted patch, subtracting the pairs whose position partner lies in it, and reapplying the two normalisations that change under delete-one (the responsivity \(2\mathcal{R}\) and the \(RR\) amplitude). The delete_one_estimator helper does all of that:

from measureia.measure_galaxy_box import delete_one_estimator, jk_columns

out = mi.measure_galaxy_contributions("ds1", num_jk=27, temp_file_path=False, return_output=True)

est_5 = delete_one_estimator(out, 5)   # realisation 5, identical to the stored one
Y_col, P_col = jk_columns(out, 5)      # what each galaxy contributes through patch 5

delete_one_estimator(out, n) reproduces multipoles_g_plus/ds1_jk27/ds1_n to floating-point summation order. Use jk_columns when you need the per-galaxy columns themselves, for instance to jackknife a fitted regression coefficient rather than the signal.

The jackknife arrays are stored sparsely: a galaxy's neighbours span a ball of \(r_\mathrm{max}\), so it reaches only a handful of sub-boxes however many there are, and the rest of the patch axis is structurally zero. Only the patches a galaxy actually has pairs in are kept, with jk_patches recording which column is which. Both helpers handle that indirection for you. The stored values are identical to the dense form — for a COLIBRE-L400-sized run (301k shape galaxies, 125 patches, 12 bins) it is 0.78 GB per array instead of 3.6 GB.

Output

Written under a galaxy_contributions group; see Output file structure for the datasets and their shapes. Pass return_output=True to get the same arrays as a dictionary instead.

The method is documented in full on the MeasureIABox API page.