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arxiv: 1907.05648 · v1 · pith:Y4NQ3SERnew · submitted 2019-07-12 · 📊 stat.CO · astro-ph.IM

rcosmo: R Package for Analysis of Spherical, HEALPix and Cosmological Data

Daniel Fryer , Ming Li , Andriy Olenko This is my paper

Pith reviewed 2026-05-24 22:12 UTC · model grok-4.3

classification 📊 stat.CO astro-ph.IM
keywords rcosmoHEALPixCMBspherical dataR packagespatial statisticscoordinate transformationcosmological data
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The pith

The rcosmo R package supplies more than 100 functions for processing, visualizing and statistically analyzing spherical data stored in HEALPix format.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents the rcosmo package, built to handle Cosmic Microwave Background radiation and other spherical observations kept in the Hierarchical Equal Area isoLatitude Pixelation scheme. It supplies coordinate conversion tools that move data from spherical, cartesian and geographic systems into the HEALPix grid, plus routines for manipulation, plotting and spatial statistics. A sympathetic reader would value the work because sphere-based measurements appear across geosciences, physics and related fields, and an R implementation lowers the barrier to routine analysis. The authors outline the package structure and illustrate selected operations together with timing benchmarks.

Core claim

rcosmo is an R package containing more than 100 functions developed for spherical data in the HEALPix representation; most functions were first written for CMB analysis yet remain applicable to any spherical dataset once the supplied conversion routines place the data into HEALPix pixels.

What carries the argument

The HEALPix pixelation scheme together with the set of coordinate transformation and spatial-analysis functions that operate on it.

If this is right

  • Spatial statistical methods for CMB data become directly usable inside standard R workflows without external language calls.
  • Data originally recorded in geographic or cartesian coordinates can be mapped into a uniform equal-area grid for consistent processing.
  • Visualization and basic manipulation of large spherical datasets can be performed with the package's built-in plotting and subsetting tools.
  • Benchmarks included in the paper indicate measurable speed advantages for the implemented operations on typical cosmological data volumes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same transformation layer could support analysis pipelines that combine CMB maps with other spherical fields such as planetary topography.
  • Extension to time-series spherical data would require only modest additions to the existing pixel-indexing machinery.
  • Because the package already handles geographic coordinates, it could serve as a bridge between astronomical and Earth-science spherical datasets.

Load-bearing premise

The supplied functions execute correctly and the reported benchmarks reflect genuine practical gains rather than implementation artifacts.

What would settle it

A user loads a public CMB map, applies the coordinate conversion and analysis routines, and obtains pixel values or statistical summaries that differ from those produced by an independent HEALPix library on the same input.

Figures

Figures reproduced from arXiv: 1907.05648 by Andriy Olenko, Daniel Fryer, Ming Li.

Figure 1
Figure 1. Figure 1: rcosmo main structure and core functions. Visualisation tools Standard Python and MATLAB tools for CMB and HEALPix visualization use the Mollweide projection of the unit sphere to the 2d plane. This is an equal-area projection, but it distorts spherical angles and distances. In contrast rcosmo employs the ‘OpenGL’ powered 3d visualization device system rgl for R to allow 3d interactive plots of data on the… view at source ↗
Figure 2
Figure 2. Figure 2: (a): HEALPix base pixel boundary visualisation. The 12 base pixels are labelled 1 to 12; (b): HEALPix nested ordering visualisation at Nside = 2. Pixels 1, 2, 3 and 4 (labelled) all fall within base pixel 1 (coloured solid). HEALPix initially divides the sphere into 12 equiareal base pixels. To visualise these with rcosmo , we can first generate a CMBDataFrame at some low resolution (e.g, Nside = 64) and t… view at source ↗
Figure 3
Figure 3. Figure 3: HEALPix ring ordering scheme visualisation. The black line traces in order through pixel centers from 1 to Npix = 768. The locations of pixels 100 to 107 are labelled. At a given Nside, the HEALPix representation provides a bijection from the first 12N2 side natural numbers P to a set of locations L on the unit sphere. We refer to P as the set of pixel indices and L as the set of pixel centers. For assigni… view at source ↗
Figure 4
Figure 4. Figure 4: All pixel centers (at resolution 5), within pixel 1 (at resolution 1) The group of rcosmo functions that includes pix2coords, pixelArea, nestSearch, etc., computes spherical geometric properties in relation to by pixel indices. For example, the nestSearch function searches a pixel closest to a point in 3d space. It uses an algorithm that achieves a high level of efficiency using the nested hierarchy. A com… view at source ↗
Figure 5
Figure 5. Figure 5: Boundary visualisation of polygon CMBWindow objects, plotted against 105 CMB intensities. Note that for the CMBWindow polygons defined above, entire polygons lie within any one hemisphere of S2. To obtain CMBWindow objects that occupy more than one hemisphere, we can specify a polygon or disc exterior (complement in S2) using the set.minus = TRUE parameter. For example, the following command gives the exte… view at source ↗
Figure 6
Figure 6. Figure 6: CMB intensity data extracted from an CMBDataFrame object by the window function. Spherical geometry functions Several basic tools for spherical geometry are implemented in rcosmo : • Converting between different coordinate systems on the sphere, • Computing geodesic distances between points and windows, • Calculating spherical angles, [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Triangulation of a spherical polygon. Statistical functions In this section we overview core statistical functions implemented in rcosmo . The package provides various tools for statistical analysis of spherical data that can be broadly divided in the following types: • Spherical random sampling, • Univariate spherical statistics and plots, • Multivariate statistics for data from different CMBWindows, • Me… view at source ↗
Figure 8
Figure 8. Figure 8: Sample Renyi function Tˆ(q) of sky.annulus on [1.01,10]. The function plotAngDis helps to visualise the marginal distributions of temperature intensities versus θ and φ angles. It produces scatterplots and barplots of the corresponding means computed over bins, see [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Distributions of temperature versus θ and φ angles for the Scorpion constellation region. Multivariate statistics for data from different CMBWindows. There are several rcosmo functions for comparison of data from two or more CMBWindows. For example, the function qqplotWin is a modification of the standard qqplot to produces a QQ plot of quantiles of observations in two CMBWindows against each other for a s… view at source ↗
Figure 10
Figure 10. Figure 10: QQ plot of observations in the Dragon vs Scorpion constellation regions. > qqplotWin(df1, polygon1, polygon2) The function qstatq can be used to measure spatial stratified heterogeneity in a list of CMBWindows. It takes values in [0, 1], where 0 corresponds to no spatial stratified heterogeneity, 1 means a perfect heterogeneity case. For example, the results below shows that there is not enough evidence f… view at source ↗
Figure 11
Figure 11. Figure 11: Plot of the Askey covariance function for the parameters σ 2 = 1, ψ = π/4, and κ = 4. Obtained estimated covariance values can be visualised using the command > plot(Cov) [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Plot of the empirical covariance function for max.dist = 0.03. The function variofitCMB estimates parameters of variogram models (see equation (3) for the link between covariance and variogram functions) by fitting a parametric model from the list covmodelCMB to a sample variogram estimated by the function variogramCMB. This function is built on and extends variofit from the package geoR to specific rcosm… view at source ↗
Figure 13
Figure 13. Figure 13: Plots of the empirical and fitted variograms [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Plot the covariance estimate using CMB power spectrum. Converting other spherical data to HEALPix format While the HEALPix is the main representation in cosmological applications there are numerous spherical data, for example, in geosciences, that use different coordinate systems and spherical formats. This example shows how non-HEALPix spherical data can be converted to the HEALPix format for rcosmo anal… view at source ↗
Figure 15
Figure 15. Figure 15: Plot of world’s large cities and towns at the resolution nside = 1024. Summary and future directions This article introduces the package rcosmo for analysis of CMB, HEALPix and other spherical data. The package integrates the HEALPix representation and various spherical geometric and statistical methods in a convenient unified framework. It opens efficient handling and analysis of HEALPix and CMB data to … view at source ↗
read the original abstract

The analysis of spatial observations on a sphere is important in areas such as geosciences, physics and embryo research, just to name a few. The purpose of the package rcosmo is to conduct efficient information processing, visualisation, manipulation and spatial statistical analysis of Cosmic Microwave Background (CMB) radiation and other spherical data. The package was developed for spherical data stored in the Hierarchical Equal Area isoLatitude Pixelation (Healpix) representation. rcosmo has more than 100 different functions. Most of them initially were developed for CMB, but also can be used for other spherical data as rcosmo contains tools for transforming spherical data in cartesian and geographic coordinates into the HEALPix representation. We give a general description of the package and illustrate some important functionalities and benchmarks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript describes the rcosmo R package, which supplies more than 100 functions for efficient processing, visualization, manipulation, and spatial statistical analysis of Cosmic Microwave Background (CMB) radiation and other spherical data stored in the HEALPix pixelization, including tools to transform data from Cartesian and geographic coordinates into HEALPix format. It provides a general overview and illustrates selected functionalities together with benchmarks.

Significance. A well-documented and validated R package for HEALPix-based spherical data analysis would be a useful addition to the statistical computing ecosystem, particularly for cosmologists and researchers in geosciences who require coordinate transformations and spatial statistics on the sphere. Reproducible benchmark results and validation tests would strengthen its practical value.

major comments (1)
  1. The central claim that rcosmo performs 'efficient' information processing rests on benchmarks that are stated to be illustrated, yet the manuscript supplies no quantitative timings, scaling results, accuracy metrics, baseline comparisons (e.g., against healpy or other R packages), or error analysis. Without these data the efficiency assertion cannot be evaluated and is load-bearing for the package's stated purpose.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive review. The single major comment is addressed point-by-point below. We agree that quantitative support for the efficiency claims is needed and will revise the manuscript to include it.

read point-by-point responses

  1. Referee: The central claim that rcosmo performs 'efficient' information processing rests on benchmarks that are stated to be illustrated, yet the manuscript supplies no quantitative timings, scaling results, accuracy metrics, baseline comparisons (e.g., against healpy or other R packages), or error analysis. Without these data the efficiency assertion cannot be evaluated and is load-bearing for the package's stated purpose.

    Authors: We agree with this assessment. Although the manuscript states that benchmarks are illustrated, the current version does not contain the quantitative timings, scaling results, accuracy metrics, or direct comparisons (e.g., to healpy) requested. In the revised manuscript we will add a new subsection (or expanded section) presenting such results, including wall-clock timings on representative CMB-sized maps, scaling with nside, error analysis for coordinate transformations, and baseline comparisons against healpy where applicable. This will directly support the efficiency claims. revision: yes

Circularity Check

0 steps flagged

No circularity: package description paper has no derivations or self-referential claims

full rationale

The paper is a straightforward description of the rcosmo R package, its >100 functions for HEALPix/spherical data processing, coordinate transformations, and illustrative benchmarks. It contains no equations, fitted parameters, predictions, uniqueness theorems, or derivation chains of any kind. The central claim (existence and utility of the package) does not reduce to any input by construction, self-citation, or renaming. This is the expected non-finding for a software paper with no mathematical content.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a software package description paper. It introduces no free parameters, mathematical axioms, or invented entities. All functionality builds on the pre-existing HEALPix representation standard.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Spherical data handling and analysis with R package rcosmo

    stat.AP 2019-07 unverdicted novelty 4.0

    rcosmo is an R package offering functions to convert and analyze geographic, point pattern, and star-shaped spherical data in HEALPix format with ready-to-use code examples.

Reference graph

Works this paper leans on

12 extracted references · 12 canonical work pages · cited by 1 Pith paper · 1 internal anchor

  1. [1]

    R. Adam, P . Ade, N. Aghanim, Y. Akrami, M. Alves, F. Argüeso, M. Arnaud, F. Arroja, M. Ashdown, J. Aumont, et al. Planck 2015 results-I. Overview of products and scientific results. Astronomy and Astrophysics, 594(A1):1–38,

    work page 2015

  2. [2]

    URL https://doi.org/10.1051/0004-6361/201527101. [p] D. Adler, D. Murdoch, and others. rgl: 3D Visualization Using OpenGL ,

    work page doi:10.1051/0004-6361/201527101

  3. [3]

    URL https://doi.org/10.1086/377253. [p] R. S. Bivand, E. Pebesma, and V . Gomez-Rubio. Applied spatial data analysis with R, Second edition . Springer, NY,

    work page doi:10.1086/377253

  4. [4]

    URL https: //doi.org/10.1111/j.1755-0998.2011.03108.x. [p] M. R. Calabretta and B. F. Roukema. Mapping on the healpix grid. Monthly Notices of the Royal Astro- nomical Society, 381(2):865–872,

    work page doi:10.1111/j.1755-0998.2011.03108.x 2011

  5. [5]

    URL https://doi.org/10.1111/j.1365-2966.2007.12297.x. [p] R. Durrer. The cosmic microwave background: the history of its experimental investigation and its significance for cosmology. Classical and Quantum Gravity , 32(12),

    work page doi:10.1111/j.1365-2966.2007.12297.x 2007

  6. [6]

    URL https://doi.org/10.1093/mnras/258.1.1P’. [p] A. Felicísimo, J. C. R. Cuetos, M. E. P . García, A. Cuartero, and P . G. Rodriguez. VecStatGraphs3D: Vector analysis using graphical and analytical methods in 3D ,

    work page doi:10.1093/mnras/258.1.1p

  7. [7]

    URL https://doi.org/10.18637/jss.v070.i06. [p] N. I. Fisher, T. Lewis, and B. J. J. Embleton. Statistical Analysis of Spherical Data . Cambridge University Press, Cambridge,

    work page doi:10.18637/jss.v070.i06

  8. [8]

    URL https://doi.org/10.3150/12-BEJSP06. [p] K. M. Gorski, E. Hivon, A. Banday, B. D. Wandelt, F. K. Hansen, M. Reinecke, and M. Bartelmann. Healpix: a framework for high-resolution discretization and fast analysis of data distributed on the sphere. The Astrophysical Journal, 622(2):759–771,

    work page doi:10.3150/12-bejsp06

  9. [9]

    URL https://doi.org/10.1086/427976. [p] A. Harris. cosmoFns: Functions for cosmological distances, times, luminosities, etc. ,

    work page internal anchor Pith review doi:10.1086/427976

  10. [10]

    URL https://doi.org/10.1051/0004- 6361/201425555. [p] L. Kelvin. astro: Astronomy Functions, T ools and Routines,

    work page doi:10.1051/0004-

  11. [11]

    URL https://doi.org/10.1142/S0218348X13500096. [p] N. Leonenko, M. Taqqu, and G. Terdik. Estimation of the covariance function of Gaussian isotropic random fields on spheres, related Rosenblatt-type distributions and the cosmic variance problem. Electron. J. Statist., 12(2):3114–3146,

    work page doi:10.1142/s0218348x13500096

  12. [12]

    URL https://doi.org/10.1214/18-EJS1473. [p] J. Liu. CRAC: Cosmology R Analysis Code ,

    work page doi:10.1214/18-ejs1473