nugundam 0.7.1

Fast angular, projected, marked, and PDF-aware two-point correlation functions

nuGUNDAM

nuGUNDAM is a package for fast two-point correlation functions in galaxy surveys.

It combines highly optimized Fortran/OpenMP counting cores with a modern, modular Python interface. The current package exposes clean, typed APIs for:

• angular and projected space auto/cross correlations
• PDF-aware projected auto/cross correlations
• marked angular/projected auto/cross correlations
• plain and/or weighted pair-counts in angular and projected space
• fully automatic bootstrap and jackknife uncertainty workflows
• generic input tables (Astropy, pandas, PyArrow, NumPy structured arrays, mappings)
• native result I/O, ASCII export, and plotting routines in 1D/2D
• split-random acceleration for LS autocorrelations

What is included

Angular API

• acf(data, random, config)
• accf(data1, data2, config, *, random1=None, random2=None)
• macf(data, random, config, *, mark=...)
• maccf(data1, data2, config, *, mark=..., random1=None, random2=None)
• ang_auto_counts(data, config)
• ang_cross_counts(data1, data2, config)

Projected API

• pcf(data, random, config)
• pccf(data1, data2, config, *, random1=None, random2=None)
• mpcf(data, random, config, *, mark=...)
• mpccf(data1, data2, config, *, mark=..., random1=None, random2=None)
• proj_auto_counts(data, config)
• proj_cross_counts(data1, data2, config)

PDF-aware projected correlations

Projected auto- and cross-correlations can propagate per-object redshift PDFs directly through the pair counts. Four modes are available:

• exact-grid (grid_chi_exact): deterministic integration of empirical PDFs on a common radial grid
• GMM (gmm_chi): deterministic compression into a small Gaussian mixture
• 16quant (quantile_chi): deterministic equal-probability quantile representation
• Monte Carlo: averages ordinary projected pair counts over redshift realizations drawn from the PDFs

All modes use the standard pcf / pccf interface and return the usual projected result objects. Resolved line-of-sight bins can be used to inspect xi(rp, pi) or to integrate the projected statistic to a selected pi_max.

Marked-correlation API

Marked correlations are implemented as a thin layer on top of the existing weighted correlation machinery. nuGUNDAM runs:

1. an ordinary unweighted branch, and
2. a mark-weighted branch where the data objects carry the processed mark values,

then combines both into the final marked statistic.

The public mark specification objects are:

• AutoMarkSpec
• CrossMarkSpec

The public marked result classes are:

• MarkedAngularCorrelationResult
• MarkedProjectedCorrelationResult

For angular auto-correlations, the default marked statistic is

[ M(\theta)=\frac{1+w_{\mathrm{marked}}(\theta)}{1+w(\theta)}. ]

For projected auto-correlations, the default marked statistic is

[ M(r_p)=\frac{1+w_{p,\mathrm{marked}}(r_p)/r_p}{1+w_p(r_p)/r_p}. ]

Only the data sample needs a mark column. Random catalogs remain unweighted, as their role is to encode the survey geometry and selection function.

Estimators

Currently implemented for both angular and projected auto/cross workflows:

• NAT: natural estimator
• DP: David-Peebles
• LS: Landy-Szalay

Result utilities

• native round-trip result I/O:
  • write_result
  • read_result
• instance methods on result/count objects:
  • .write(...)
  • .save(...)
  • .to_ascii(...)
  • .plot(...)
  • .plot2d(...) for projected 2D views
  • .plot_cov_matrix(...)
  • .plot_corr_matrix(...)
• marked result helpers:
  • .plain_wtheta, .weighted_wtheta on marked angular results
  • .plain_wp, .weighted_wp on marked projected results

Plotting routines

• plotcf
• plot_result
• plotcf2d
• plot_result2d
• plot_compare_ratio
• plot_cov_matrix
• plot_corr_matrix
• plot_jk_regions

Installation

Editable install:

pip install -e .

Developer install with tests:

pip install -e .[dev]
pytest

Build notes

The package uses:

• scikit-build-core
• numpy.f2py
• CMake
• a working Fortran compiler
• OpenMP when available

The compiled extension is built from:

• src/nugundam/cflibfor.f90
• src/nugundam/cflibfor.pyf

Supported input catalogs

The public APIs accept several tabular backends as long as the required columns are present:

• Astropy tables
• pandas DataFrames
• PyArrow tables
• NumPy structured arrays / recarrays
• plain mappings of column names to arrays

The Python preparation layer extracts the requested columns once and then hands plain NumPy arrays to the compiled counters.

Public configuration objects

nuGUNDAM uses dataclass-based configs to handle the various parameters and options.

Angular:

• CatalogColumns
• AngularBinning
• AngularGridSpec
• WeightSpec
• BootstrapSpec
• JackknifeSpec
• ProgressSpec
• SplitRandomSpec
• AngularAutoConfig
• AngularCrossConfig
• AngularAutoCountsConfig
• AngularCrossCountsConfig

Projected:

• ProjectedCatalogColumns
• ProjectedBinning
• ProjectedGridSpec
• DistanceSpec
• ProjectedAutoConfig
• ProjectedCrossConfig
• ProjectedAutoCountsConfig
• ProjectedCrossCountsConfig

Marked correlations:

• AutoMarkSpec
• CrossMarkSpec

A convenient way to inspect config schemas is:

from nugundam import AngularAutoConfig, ProjectedAutoConfig

AngularAutoConfig.describe(recursive=True)
ProjectedAutoConfig.describe(recursive=True)

This prints a readable summary of nested options and defaults.

For the binning classes themselves, AngularBinning.describe() and ProjectedBinning.describe() document the available named constructors and the resolved inspection helpers such as edges, centers, widths, sepmax, rp_edges, and pi_edges.

Binning construction and inspection

The binning classes support two explicit ways to define bins:

1. from_binsize(...): define the lower bound, number of bins, and bin size.
2. from_limits(...): define the lower and upper bounds, and let nuGUNDAM derive the step.

This applies to both angular and projected workflows.

Angular binning from a bin size

from nugundam import AngularBinning

binning = AngularBinning.from_binsize(
    nsep=21,
    sepmin=0.000277778,
    dsep=0.17,
    logsep=True,
)

print(binning)
print(binning.table())

edges = binning.edges
centers = binning.centers
sepmax = binning.sepmax

Angular binning from explicit limits

from nugundam import AngularBinning

binning = AngularBinning.from_limits(
    nsep=21,
    sepmin=0.000277778,
    sepmax=1.0,
    logsep=True,
)

Projected binning from a bin size

from nugundam import ProjectedBinning

binning = ProjectedBinning.from_binsize(
    nsepp=16,
    seppmin=0.1,
    dsepp=0.15,
    logsepp=True,
    nsepv=20,
    dsepv=2.0,
)

print(binning)
print(binning.table("rp"))
print(binning.table("pi"))

rp_edges = binning.rp_edges
pi_edges = binning.pi_edges
seppmax = binning.seppmax
sepvmax = binning.sepvmax

Projected binning from explicit limits

from nugundam import ProjectedBinning

binning = ProjectedBinning.from_limits(
    nsepp=16,
    seppmin=0.1,
    seppmax=10.0,
    logsepp=True,
    nsepv=20,
    dsepv=2.0,
)

Quick start: angular auto-correlation

from nugundam import (
    AngularAutoConfig,
    CatalogColumns,
    AngularBinning,
    AngularGridSpec,
    WeightSpec,
    BootstrapSpec,
    acf,
)

cfg = AngularAutoConfig(
    estimator="LS",
    columns_data=CatalogColumns(ra="ra", dec="dec", weight="wei"),
    columns_random=CatalogColumns(ra="ra", dec="dec"),
    binning=AngularBinning.from_binsize(
        nsep=21,
        sepmin=0.000277778,
        dsep=0.17,
        logsep=True,
    ),
    grid=AngularGridSpec(
        autogrid=True,
        pxorder="cell-dec",
    ),
    weights=WeightSpec(weight_mode="auto"),
    bootstrap=BootstrapSpec(enabled=False),
    nthreads=8,
)

res = acf(data, random, cfg)

The returned object is an AngularCorrelationResult with fields such as:

• theta_edges
• theta_centers
• wtheta
• wtheta_err
• estimator
• counts
• metadata

Quick start: angular cross-correlation

from nugundam import (
    AngularCrossConfig,
    CatalogColumns,
    AngularBinning,
    AngularGridSpec,
    WeightSpec,
    BootstrapSpec,
    accf,
)

cfg = AngularCrossConfig(
    estimator="LS",
    columns_data1=CatalogColumns(ra="ra_gal", dec="dec_gal", weight="wei_gal"),
    columns_random1=CatalogColumns(ra="ra_r1", dec="dec_r1"),
    columns_data2=CatalogColumns(ra="ra_qso", dec="dec_qso", weight="wei_qso"),
    columns_random2=CatalogColumns(ra="ra_r2", dec="dec_r2"),
    binning=AngularBinning.from_binsize(nsep=21, sepmin=0.000277778, dsep=0.17, logsep=True),
    grid=AngularGridSpec(autogrid="legacy", pxorder="natural"),
    weights=WeightSpec(weight_mode="auto"),
    bootstrap=BootstrapSpec(enabled=False),
    nthreads=8,
)

res = accf(data1, data2, cfg, random1=random1, random2=random2)

Notes:

• For NAT and LS, provide both random1 and random2.
• For DP, the required random catalog depends on config.bootstrap.primary ("data1" by default).

Quick start: projected auto-correlation

from nugundam import (
    ProjectedAutoConfig,
    ProjectedCatalogColumns,
    ProjectedBinning,
    ProjectedGridSpec,
    DistanceSpec,
    WeightSpec,
    BootstrapSpec,
    pcf,
)

cfg = ProjectedAutoConfig(
    estimator="LS",
    columns_data=ProjectedCatalogColumns(
        ra="ra",
        dec="dec",
        redshift="z",
        weight="wei",
    ),
    columns_random=ProjectedCatalogColumns(
        ra="ra",
        dec="dec",
        redshift="z",
    ),
    binning=ProjectedBinning.from_binsize(
        nsepp=16,
        seppmin=0.1,
        dsepp=0.15,
        logsepp=True,
        nsepv=20,
        dsepv=2.0,
    ),
    grid=ProjectedGridSpec(
        autogrid=True,
        pxorder="natural",
    ),
    distance=DistanceSpec(
        calcdist=True,
        h0=100.0,
        omegam=0.3,
        omegal=0.7,
    ),
    weights=WeightSpec(weight_mode="auto"),
    bootstrap=BootstrapSpec(enabled=False),
    nthreads=8,
)

res = pcf(data, random, cfg)

The returned object is a ProjectedCorrelationResult with fields such as:

• rp_edges
• rp_centers
• wp
• wp_err
• estimator
• counts
• metadata

If you already have comoving distances in the catalog, set DistanceSpec(calcdist=False) and point ProjectedCatalogColumns.distance to that column.

Quick start: PDF-aware projected auto-correlation

Start from an ordinary ProjectedAutoConfig, then attach a common redshift grid and a PDF matrix whose rows follow the data catalog order. For example, the default 16-quantile mode can be enabled as follows:

from copy import deepcopy
from nugundam import PDFSourceSpec, pcf

cfg_pdf = deepcopy(cfg)
cfg_pdf.pdf.enabled = True
cfg_pdf.pdf.kind = "quantile_chi"
cfg_pdf.pdf.nquant = 16
cfg_pdf.pdf.random_pdf_policy = "inherit"

cfg_pdf.pdf_source.enabled = True
cfg_pdf.pdf_source.z_grid = z_grid       # centers or edges
cfg_pdf.pdf_source.grid_kind = "edges"
cfg_pdf.pdf_source.pdf_data = PDFSourceSpec(
    kind="external_matrix",
    matrix=pdf_matrix,                   # shape: (n_data, n_zbins)
)

res_pdf = pcf(data, random, cfg_pdf)

The same input can be used with the other deterministic modes by changing:

cfg_pdf.pdf.kind = "grid_chi_exact"      # exact empirical-PDF integration
cfg_pdf.pdf.kind = "gmm_chi"             # Gaussian-mixture compression
cfg_pdf.pdf.k = 3                         # number of GMM components

Monte Carlo uses the separate mc_pdf block:

cfg_mc = deepcopy(cfg)
cfg_mc.mc_pdf.enabled = True
cfg_mc.mc_pdf.nreal = 25
cfg_mc.mc_pdf.seed = 12345
cfg_mc.mc_pdf.random_mode = "inherit_realization"
cfg_mc.mc_pdf.sample_within_bin = True
cfg_mc.mc_pdf.z_grid = z_grid
cfg_mc.mc_pdf.grid_kind = "edges"
cfg_mc.mc_pdf.pdf_data = PDFSourceSpec(
    kind="external_matrix",
    matrix=pdf_matrix,
)

res_mc = pcf(data, random, cfg_mc)

For compiled deterministic modes, random catalogs normally inherit PDF assignments from the associated data sample; an independent random-PDF matrix is therefore not required for the usual auto-correlation workflow.

Quick start: projected cross-correlation

from nugundam import (
    ProjectedCrossConfig,
    ProjectedCatalogColumns,
    ProjectedBinning,
    ProjectedGridSpec,
    DistanceSpec,
    WeightSpec,
    BootstrapSpec,
    pccf,
)

cfg = ProjectedCrossConfig(
    estimator="LS",
    columns_data1=ProjectedCatalogColumns(ra="ra1", dec="dec1", redshift="z1", weight="w1"),
    columns_random1=ProjectedCatalogColumns(ra="rar1", dec="decr1", redshift="zr1"),
    columns_data2=ProjectedCatalogColumns(ra="ra2", dec="dec2", redshift="z2", weight="w2"),
    columns_random2=ProjectedCatalogColumns(ra="rar2", dec="decr2", redshift="zr2"),
    binning=ProjectedBinning.from_binsize(nsepp=16, seppmin=0.1, dsepp=0.15, logsepp=True, nsepv=20, dsepv=2.0),
    grid=ProjectedGridSpec(autogrid=True, pxorder="natural"),
    distance=DistanceSpec(calcdist=True),
    weights=WeightSpec(weight_mode="auto"),
    bootstrap=BootstrapSpec(enabled=False),
    nthreads=8,
)

res = pccf(data1, data2, cfg, random1=random1, random2=random2)

Quick start: marked projected auto-correlation

from nugundam import (
    ProjectedAutoConfig,
    ProjectedCatalogColumns,
    ProjectedBinning,
    ProjectedGridSpec,
    DistanceSpec,
    WeightSpec,
    BootstrapSpec,
    AutoMarkSpec,
    mpcf,
)

cfg = ProjectedAutoConfig(
    estimator="LS",
    columns_data=ProjectedCatalogColumns(ra="ra", dec="dec", redshift="z"),
    columns_random=ProjectedCatalogColumns(ra="ra", dec="dec", redshift="z"),
    binning=ProjectedBinning.from_binsize(
        nsepp=28,
        seppmin=0.02,
        dsepp=0.12,
        logsepp=True,
        nsepv=4,
        dsepv=10.0,
    ),
    grid=ProjectedGridSpec(autogrid=True, pxorder="natural"),
    weights=WeightSpec(weight_mode="unweighted"),
    bootstrap=BootstrapSpec(enabled=True, nbts=50, bseed=12345),
    distance=DistanceSpec(calcdist=True, h0=100.0, omegam=0.25, omegal=0.75),
    nthreads=4,
)

mres = mpcf(
    data,
    random,
    cfg,
    mark=AutoMarkSpec(column="GMR", normalize="mean"),
)

The returned object is a MarkedProjectedCorrelationResult with fields such as:

• rp_edges
• rp_centers
• mrp
• mrp_err
• plain
• weighted
• metadata

Useful convenience properties include:

• mres.plain_wp
• mres.weighted_wp

The same pattern applies to macf, maccf, and mpccf.

Mark specifications

AutoMarkSpec

AutoMarkSpec controls how a per-object mark is read and preprocessed before it is used as the weight in the marked branch.

Main options:

• column: data-table column containing the mark
• normalize: one of "mean", "median", or "none"
• transform: one of "identity" or "rank"
• clip: optional (lo, hi) clipping interval
• missing: either "raise" or "drop"

Typical example:

mark = AutoMarkSpec(
    column="D4000",
    normalize="mean",
    transform="identity",
    clip=None,
    missing="raise",
)

CrossMarkSpec

For cross-correlations, CrossMarkSpec lets you mark sample 1, sample 2, or both.

Main options:

• column1, column2
• mark_on: "data1", "data2", or "both"
• normalize, transform, clip, missing

Count-only APIs

The count-only APIs use dedicated configs so you need to specify only the required columns.

Angular count-only

from nugundam import (
    AngularAutoCountsConfig,
    AngularCrossCountsConfig,
    CatalogColumns,
    AngularBinning,
    AngularGridSpec,
    WeightSpec,
    BootstrapSpec,
    ang_auto_counts,
    ang_cross_counts,
)

cfg_dd = AngularAutoCountsConfig(
    columns=CatalogColumns(ra="ra", dec="dec", weight="wei"),
    binning=AngularBinning.from_binsize(nsep=21, sepmin=0.000277778, dsep=0.17, logsep=True),
    grid=AngularGridSpec(autogrid="legacy", pxorder="cell-dec"),
    weights=WeightSpec(weight_mode="auto"),
    bootstrap=BootstrapSpec(enabled=False),
    nthreads=8,
)

dd = ang_auto_counts(data, cfg_dd)

cfg_x = AngularCrossCountsConfig(
    columns1=CatalogColumns(ra="ra1", dec="dec1", weight="w1"),
    columns2=CatalogColumns(ra="ra2", dec="dec2", weight="w2"),
    binning=AngularBinning.from_binsize(nsep=21, sepmin=0.000277778, dsep=0.17, logsep=True),
    grid=AngularGridSpec(autogrid="legacy", pxorder="cell-dec"),
    weights=WeightSpec(weight_mode="auto"),
    bootstrap=BootstrapSpec(enabled=False),
    nthreads=8,
)

x = ang_cross_counts(data1, data2, cfg_x)

Projected count-only

from nugundam import (
    ProjectedAutoCountsConfig,
    ProjectedCrossCountsConfig,
    ProjectedCatalogColumns,
    ProjectedBinning,
    ProjectedGridSpec,
    DistanceSpec,
    WeightSpec,
    BootstrapSpec,
    proj_auto_counts,
    proj_cross_counts,
)

cfg_dd = ProjectedAutoCountsConfig(
    columns=ProjectedCatalogColumns(ra="ra", dec="dec", redshift="z", weight="wei"),
    binning=ProjectedBinning.from_binsize(nsepp=16, seppmin=0.1, dsepp=0.15, logsepp=True, nsepv=20, dsepv=2.0),
    grid=ProjectedGridSpec(autogrid=True, pxorder="natural"),
    distance=DistanceSpec(calcdist=True),
    weights=WeightSpec(weight_mode="auto"),
    bootstrap=BootstrapSpec(enabled=False),
    nthreads=8,
)

dd = proj_auto_counts(data, cfg_dd)

Projected count objects also keep the underlying 2D (r_p, \pi) count grids and the integrated intpi_* arrays used for projected estimators.

Weight handling

The current weighting model is:

• real data catalogs may carry object weights
• random catalogs remain unweighted
• weight_mode may be:
  • "auto"
  • "weighted"
  • "unweighted"

"auto" uses a slightly faster unweighted counter when all relevant weights are unity.

For marked correlations, the wrapper manages the weighted branch internally, so the mark itself should be passed through AutoMarkSpec or CrossMarkSpec, not through the regular weight= column definition.

Bootstrap and jackknife

Bootstrap

Bootstrap is supported in the refactored correlation and count pipelines.

Key options live in BootstrapSpec:

• enabled
• nbts
• bseed
• mode
• primary

Cross-correlation bootstrap defaults to a primary-sample scheme.

For marked correlations, nuGUNDAM computes the marked bootstrap realizations from matched plain and weighted resamples, rather than combining already-compressed error bars afterward.

Jackknife

Jackknife is currently supported for the full correlation APIs:

• acf
• accf
• pcf
• pccf
• macf
• maccf
• mpcf
• mpccf

If no explicit region column is supplied, the package can generate sky regions automatically using a k-means-based partitioner. Jackknife-aware results can carry:

• covariance matrices
• leave-one-region-out realizations
• metadata describing the region source and fast-path usage

Marked jackknife covariances are built from matched marked realizations.

Jackknife plotting routines

• plot_cov_matrix
• plot_corr_matrix
• plot_jk_regions

Examples:

ax = res.plot_cov_matrix()
ax = res.plot_corr_matrix()

To visualize the generated jackknife sky regions:

from nugundam import plot_jk_regions

ax = plot_jk_regions(data=data, random=random, config=cfg, catalog="data")

Split-random RR acceleration

nuGUNDAM includes split-random support for the LS estimator in autocorrelation in both angular and projected space. This feature is configured through SplitRandomSpec and is intended to reduce the cost of the RR term by splitting the random catalog into shuffled chunks, counting RR pairs in each, accumulating and properly normalizing these counts before combining them into the total estimator.

Modes:

• match_data
• nchunks
• chunk_size

Example:

from nugundam import SplitRandomSpec

cfg.split_random = SplitRandomSpec(
    enabled=True,
    mode="match_data",
    seed=12345,
)

By default, split-random operates in match_data mode, creating as many RR chunks as needed, each roughly the size of the data sample. Split-random is not available together with jackknife.

Grid selection and preparatory ordering

Angular grid modes

AngularGridSpec.autogrid accepts:

• True or "legacy" for the original nuGUNDAM heuristic
• False for fully manual mxh1/mxh2
• "adaptive" for the newer runtime-aware count-box probe

Angular pxorder

Supported values:

• "cell-dec"
• "natural"
• "none"

"cell-dec" adds an intra-cell declination sort on top of the counter-cell ordering.

Projected grid modes

Projected space currently keeps the legacy boolean autogrid choice:

• True
• False

Projected pxorder currently supports:

• "natural"
• "none"

Progress reporting

Progress behavior is controlled through ProgressSpec.

Typical defaults:

• compact notebook status updates
• direct streaming output in terminal sessions

Example:

cfg.progress.enabled = True
cfg.progress.progress_file = None
cfg.progress.poll_interval = 0.2

To keep a progress file:

cfg.progress.progress_file = "run.progress"

To silence progress:

cfg.progress.enabled = False

Result persistence

The native on-disk format is a single compressed file containing arrays and embedded JSON metadata/config/provenance.

Top-level auxiliary functions:

from nugundam import write_result, read_result

write_result(res, "run.gres")
res2 = read_result("run.gres")

Instance methods:

res.save("run.gres")
res.write("run.gres")
res2 = type(res).read_result("run.gres")

Round-tripped results preserve:

• the result class
• nested count objects
• numeric arrays
• stored metadata
• original run configuration
• provenance information

This includes marked result classes and their nested plain/weighted branches.

ASCII export

Result and count objects can be exported to plain ASCII:

res.to_ascii("acf.txt")

The default exported columns are chosen from the object type and estimator. To control which columns are exported, customize the cols keyword:

res.to_ascii(
    "acf_custom.txt",
    cols=["theta_centers", "dd", "rr", "dr", "wtheta", "wtheta_err"],
)

Marked results can likewise be exported with their default marked columns or with an explicit custom column list.

Plotting

1D plotting from result objects

Result objects can be plotted directly using their attached plot() method, either on a new figure or inserted into a pre-existing axis:

res.plot(color="r", label="sample A", errors="bar")

import matplotlib.pyplot as plt

fig, ax = plt.subplots()
res.plot(ax=ax, color="r", label="sample A", errors="bar")
ax.legend()

Supported uncertainty styles:

• errors="bar"
• errors="band"
• errors="none"

Marked results follow the same interface:

mres.plot(label="marked", errors="bar")

1D plotting from raw arrays

from nugundam import plotcf

ax = plotcf(theta, wtheta, yerr=werr, errors="band")

Overlaying several curves

fig, ax = plt.subplots()

res1.plot(ax=ax, label="sample 1", color="tab:blue")
res2.plot(ax=ax, label="sample 2", errors="band", color="tab:orange",
          band_kwargs={"alpha": 0.15})

ax.legend()

Projected 2D plotting

Projected results and projected count objects can be visualized in 2D. They have options to overlay contours and smooth the resulting map:

ax = res.plot2d(which="xi")

Low-level auxiliary functions are also available:

• plotcf2d
• plot_result2d

Ratio comparison plotting

The function plot_compare_ratio builds a two-panel comparison plot with shared axes, which supports several correlation curves on top and multiple curve ratios below.

Package layout

src/nugundam/
├── angular/
├── projected/
├── core/
├── io.py
├── ascii_io.py
├── plotting.py
├── angular_public.py
├── projected_public.py
├── marked.py
├── result_meta.py
├── cflibfor.f90
└── cflibfor.pyf