Using Firecrown to Generate Two-Point Statistics for LSST

Version ?env:FIRECROWN_VERSION

Authors

Marc Paterno

Sandro Vitenti

Purpose of this Document

In the tutorial redshift distributions we illustrate the process of using Firecrown to create redshift distributions based on specified parameters describing the distributions. Additionally, in serializable redshift distributions we demonstrate how to generate redshift distributions using serializable objects. This document outlines how to use InferredGalaxyZDist objects to derive the two-point statistics pertinent to the Large Synoptic Survey Telescope (LSST), employing the redshift distribution outlined in the LSST Science Requirements Document (SRD).

This tutorial focuses on generating two-point statistics from scratch using metadata. For loading existing data from SACC files and applying scale cuts, see: - Two-Point Factory Basics - Loading SACC Data - Scale Cuts and Filtering

Two-point statistics

Two-point statistics are widely used in cosmological analyses. They provide a statistical summary of the distribution, in either real or harmonic space, of galaxies and the matter density field, or of other observables. In Firecrown, two-point statistics are represented by the TwoPoint class, in the module firecrown.likelihood.

Note: This tutorial demonstrates generating two-point statistics from scratch. If you have existing data in a SACC file, see Loading SACC Data for how to extract and use it.

Generating the LSST Year 1 Redshift Distribution Bins

Our initial step involves generating all photometric redshift bins necessary for the LSST year 1 redshift distribution. This process is detailed here in the tutorial on redshift distributions. In the serialization tutorial, we demonstrate how to get the LSST SRD redshift distributions. Here we will use the LSST SRD year 1 redshift distribution to generate the two-point statistics.

from firecrown.generators import (
    LSST_Y1_LENS_HARMONIC_BIN_COLLECTION,
    LSST_Y1_SOURCE_HARMONIC_BIN_COLLECTION,
)

count_bins = LSST_Y1_LENS_HARMONIC_BIN_COLLECTION.generate()
shear_bins = LSST_Y1_SOURCE_HARMONIC_BIN_COLLECTION.generate()
all_y1_bins = count_bins + shear_bins

Generating the Two-Point Metadata

Within firecrown.metadata_functions, a suite of functions is available to calculate all possible two-point statistic metadata corresponding to a designated set of bins. The data classes themselves live in firecrown.metadata_types. For instance, demonstrated below is the computation of all feasible metadata tailored to the LSST year 1 redshift distribution:

import numpy as np
from firecrown.metadata_functions import make_all_photoz_bin_combinations
from firecrown.metadata_types import TwoPointHarmonic

all_two_point_xy = make_all_photoz_bin_combinations(all_y1_bins)
ells = np.unique(np.geomspace(2, 2000, 128).astype(int))
all_two_point_cells = [TwoPointHarmonic(XY=xy, ells=ells) for xy in all_two_point_xy]

Filtering with Bin Pair Selectors: If you only need specific subsets of correlations (e.g., only auto-correlations, only source measurements, or custom combinations), you can use BinPairSelector objects to filter the pairs during generation. See Bin Pair Selectors for details on how to control which bin pairs are included.

The code above generates the following table of two-point statistic metadata:

Code 
import pandas as pd
from IPython.display import Markdown

two_point_names = [
    (Cells.XY.x.bin_name, Cells.XY.y.bin_name, Cells.get_sacc_name())
    for Cells in all_two_point_cells
]
df = pd.DataFrame(two_point_names, columns=["bin-x", "bin-y", "SACC data-type"])
Markdown(df.to_markdown())
bin-x bin-y SACC data-type
0 lsst_y1_source0 lsst_y1_source0 galaxy_shear_cl_ee
1 lsst_y1_source0 lsst_y1_source1 galaxy_shear_cl_ee
2 lsst_y1_source0 lsst_y1_source2 galaxy_shear_cl_ee
3 lsst_y1_source0 lsst_y1_source3 galaxy_shear_cl_ee
4 lsst_y1_source0 lsst_y1_source4 galaxy_shear_cl_ee
5 lsst_y1_source1 lsst_y1_source1 galaxy_shear_cl_ee
6 lsst_y1_source1 lsst_y1_source2 galaxy_shear_cl_ee
7 lsst_y1_source1 lsst_y1_source3 galaxy_shear_cl_ee
8 lsst_y1_source1 lsst_y1_source4 galaxy_shear_cl_ee
9 lsst_y1_source2 lsst_y1_source2 galaxy_shear_cl_ee
10 lsst_y1_source2 lsst_y1_source3 galaxy_shear_cl_ee
11 lsst_y1_source2 lsst_y1_source4 galaxy_shear_cl_ee
12 lsst_y1_source3 lsst_y1_source3 galaxy_shear_cl_ee
13 lsst_y1_source3 lsst_y1_source4 galaxy_shear_cl_ee
14 lsst_y1_source4 lsst_y1_source4 galaxy_shear_cl_ee
15 lsst_y1_source0 lsst_y1_lens0 galaxy_shearDensity_cl_e
16 lsst_y1_source0 lsst_y1_lens1 galaxy_shearDensity_cl_e
17 lsst_y1_source0 lsst_y1_lens2 galaxy_shearDensity_cl_e
18 lsst_y1_source0 lsst_y1_lens3 galaxy_shearDensity_cl_e
19 lsst_y1_source0 lsst_y1_lens4 galaxy_shearDensity_cl_e
20 lsst_y1_source1 lsst_y1_lens0 galaxy_shearDensity_cl_e
21 lsst_y1_source1 lsst_y1_lens1 galaxy_shearDensity_cl_e
22 lsst_y1_source1 lsst_y1_lens2 galaxy_shearDensity_cl_e
23 lsst_y1_source1 lsst_y1_lens3 galaxy_shearDensity_cl_e
24 lsst_y1_source1 lsst_y1_lens4 galaxy_shearDensity_cl_e
25 lsst_y1_source2 lsst_y1_lens0 galaxy_shearDensity_cl_e
26 lsst_y1_source2 lsst_y1_lens1 galaxy_shearDensity_cl_e
27 lsst_y1_source2 lsst_y1_lens2 galaxy_shearDensity_cl_e
28 lsst_y1_source2 lsst_y1_lens3 galaxy_shearDensity_cl_e
29 lsst_y1_source2 lsst_y1_lens4 galaxy_shearDensity_cl_e
30 lsst_y1_source3 lsst_y1_lens0 galaxy_shearDensity_cl_e
31 lsst_y1_source3 lsst_y1_lens1 galaxy_shearDensity_cl_e
32 lsst_y1_source3 lsst_y1_lens2 galaxy_shearDensity_cl_e
33 lsst_y1_source3 lsst_y1_lens3 galaxy_shearDensity_cl_e
34 lsst_y1_source3 lsst_y1_lens4 galaxy_shearDensity_cl_e
35 lsst_y1_source4 lsst_y1_lens0 galaxy_shearDensity_cl_e
36 lsst_y1_source4 lsst_y1_lens1 galaxy_shearDensity_cl_e
37 lsst_y1_source4 lsst_y1_lens2 galaxy_shearDensity_cl_e
38 lsst_y1_source4 lsst_y1_lens3 galaxy_shearDensity_cl_e
39 lsst_y1_source4 lsst_y1_lens4 galaxy_shearDensity_cl_e
40 lsst_y1_lens0 lsst_y1_lens0 galaxy_density_cl
41 lsst_y1_lens0 lsst_y1_lens1 galaxy_density_cl
42 lsst_y1_lens0 lsst_y1_lens2 galaxy_density_cl
43 lsst_y1_lens0 lsst_y1_lens3 galaxy_density_cl
44 lsst_y1_lens0 lsst_y1_lens4 galaxy_density_cl
45 lsst_y1_lens1 lsst_y1_lens1 galaxy_density_cl
46 lsst_y1_lens1 lsst_y1_lens2 galaxy_density_cl
47 lsst_y1_lens1 lsst_y1_lens3 galaxy_density_cl
48 lsst_y1_lens1 lsst_y1_lens4 galaxy_density_cl
49 lsst_y1_lens2 lsst_y1_lens2 galaxy_density_cl
50 lsst_y1_lens2 lsst_y1_lens3 galaxy_density_cl
51 lsst_y1_lens2 lsst_y1_lens4 galaxy_density_cl
52 lsst_y1_lens3 lsst_y1_lens3 galaxy_density_cl
53 lsst_y1_lens3 lsst_y1_lens4 galaxy_density_cl
54 lsst_y1_lens4 lsst_y1_lens4 galaxy_density_cl

Summary

You now have metadata for all LSST Year 1 two-point statistics. The key outputs are:

  • all_y1_bins: Redshift distributions for all lens and source bins
  • all_two_point_xy: All possible tracer pair combinations
  • all_two_point_cells: Complete harmonic-space metadata (layouts)

These metadata objects contain no observational data—they describe the structure of measurements you want to analyze.

Next Steps

To construct TwoPoint objects from this metadata and compute predictions: