Results 1001-1050 of 2032 (2002 ASCL, 30 submitted)

[ascl:1504.008]
MCSpearman: Monte Carlo error analyses of Spearman's rank test

Spearman’s rank correlation test is commonly used in astronomy to discern whether a set of two variables are correlated or not. Unlike most other quantities quoted in astronomical literature, the Spearman’s rank correlation coefficient is generally quoted with no attempt to estimate the errors on its value. This code implements a number of Monte Carlo based methods to estimate the uncertainty on the Spearman’s rank correlation coefficient.

[ascl:1504.007]
WebbPSF: James Webb Space Telescope PSF Simulation Tool

Perrin, Marshall D.; Long, Joseph; Sivaramakrishnan, Anand; Lajoie, Charles-Phillipe; Elliot, Erin; Pueyo, Laurent; Albert, Loic

WebbPSF provides a PSF simulation tool in a flexible and easy-to-use software package implemented in Python. Functionality includes support for spectroscopic modes of JWST NIRISS, MIRI, and NIRSpec, including modeling of slit losses and diffractive line spread functions.

[ascl:1504.006]
drive-casa: Python interface for CASA scripting

drive-casa provides a Python interface for scripting of CASA (ascl:1107.013) subroutines from a separate Python process, allowing for utilization alongside other Python packages which may not easily be installed into the CASA environment. This is particularly useful for embedding use of CASA subroutines within a larger pipeline. drive-casa runs plain-text casapy scripts directly; alternatively, the package includes a set of convenience routines which try to adhere to a consistent style and make it easy to chain together successive CASA reduction commands to generate a command-script programmatically.

[ascl:1504.005]
chimenea: Multi-epoch radio-synthesis data imaging

Chimenea implements an heuristic algorithm for automated imaging of multi-epoch radio-synthesis data. It generates a deep image via an iterative Clean subroutine performed on the concatenated visibility set and locates steady sources in the field of view. The code then uses this information to apply constrained and then unconstrained (*i.e.*, masked/open-box) Cleans to the single-epoch observations. This obtains better results than if the single-epoch data had been processed independently without prior knowledge of the sky-model. The chimenea pipeline is built upon CASA (ascl:1107.013) subroutines, interacting with the CASA environment via the drive-casa (ascl:1504.006) interface layer.

[ascl:1504.004]
HOTPANTS: High Order Transform of PSF ANd Template Subtraction

HOTPANTS (High Order Transform of PSF ANd Template Subtraction) implements the Alard 1999 algorithm for image subtraction. It photometrically aligns one input image with another after they have been astrometrically aligned.

[ascl:1504.003]
EsoRex: ESO Recipe Execution Tool

EsoRex (ESO Recipe Execution Tool) lists, configures, and executes Common Pipeline Library (CPL) (ascl:1402.010) recipes from the command line. Its features include automatically generating configuration files, recursive recipe-path searching, command line and configuration file parameters, and recipe product naming control, among many others.

[ascl:1504.002]
SPA: Solar Position Algorithm

The Solar Position Algorithm (SPA) calculates the solar zenith and azimuth angles in the period from the year -2000 to 6000, with uncertainties of +/- 0.0003 degrees based on the date, time, and location on Earth. SPA is implemented in C; in addition to being available for download, an online calculator using this code is available at http://www.nrel.gov/midc/solpos/spa.html.

[ascl:1504.001]
UPMASK: Unsupervised Photometric Membership Assignment in Stellar Clusters

UPMASK, written in R, performs membership assignment in stellar clusters. It uses photometry and spatial positions, but can take into account other types of data. UPMASK takes into account arbitrary error models; the code is unsupervised, data-driven, physical-model-free and relies on as few assumptions as possible. The approach followed for membership assessment is based on an iterative process, principal component analysis, a clustering algorithm and a kernel density estimation.

[ascl:1503.011]
VESPA: False positive probabilities calculator

Validation of Exoplanet Signals using a Probabilistic Algorithm (VESPA) calculates false positive probabilities and statistically validates transiting exoplanets. Written in Python, it uses isochrones [ascl:1503.010] and the package simpledist.

[ascl:1503.010]
isochrones: Stellar model grid package

Isochrones, written in Python, simplifies common tasks often done with stellar model grids, such as simulating synthetic stellar populations, plotting evolution tracks or isochrones, or estimating the physical properties of a star given photometric and/or spectroscopic observations.

[ascl:1503.009]
GSD: Global Section Datafile access library

Tilanus, Remo; Meyerdierks, Horst; Jenness, Tim; Fairclough, Jon; Padman, Rachael; Redman, Russell; Cockayne, Steve

The GSD library reads data written in the James Clerk Maxwell Telescope GSD format. This format uses the General Single-Dish Data model and was used at the JCMT until 2005. The library provides an API to open GSD files and read their contents. The content of the data files is self-describing and the library can return the type and name of any component. The library is used by SPECX (ascl:1310.008), JCMTDR (ascl:1406.019) and COADD (ascl:1411.020). The SMURF (ascl:1310.007) package can convert GSD heterodyne data files to ACSIS format using this library.

[ascl:1503.008]
pYSOVAR: Lightcurves analysis

The pYSOVAR code calculates properties for a stack of lightcurves, including simple descriptive statistics (mean, max, min, ...), timing (e.g. Lomb-Scargle periodograms), variability indixes (e.g. Stetson), and color properties (e.g. slope in the color-magnitude diagram). The code is written in python and is closely integrated with astropy tables. Initially, pYSOVAR was written specifically for the analysis of two clusters in the YSOVAR project, using the (not publicly released) YSOVAR database as an input. Additional functionality has been added and the code has become more general; it is now useful for other clusters in the YSOVAR dataset or for other projects that have similar data (lightcurves in one or more bands with a few hundred points for a few thousand objects), though may not work out-of-the-box for different datasets.

[ascl:1503.007]
UniPOPS: Unified data reduction suite

Maddalena, Ronald J.; Garwood, Robert W.; Salter, Christopher J.; Stobie, Elizabeth B; Cram, Thomas R.; Morgan, Lorrie; Vance, Bob; Hudson, Jerome

UniPOPS, a suite of programs and utilities developed at the National Radio Astronomy Observatory (NRAO), reduced data from the observatory's single-dish telescopes: the Tucson 12-m, the Green Bank 140-ft, and archived data from the Green Bank 300-ft. The primary reduction programs, 'line' (for spectral-line reduction) and 'condar' (for continuum reduction), used the People-Oriented Parsing Service (POPS) as the command line interpreter. UniPOPS unified previous analysis packages and provided new capabilities; development of UniPOPS continued within the NRAO until 2004 when the 12-m was turned over to the Arizona Radio Observatory (ARO). The submitted code is version 3.5 from 2004, the last supported by the NRAO.

[ascl:1503.006]
AMADA: Analysis of Multidimensional Astronomical DAtasets

AMADA allows an iterative exploration and information retrieval of high-dimensional data sets. This is done by performing a hierarchical clustering analysis for different choices of correlation matrices and by doing a principal components analysis in the original data. Additionally, AMADA provides a set of modern visualization data-mining diagnostics. The user can switch between them using the different tabs.

[ascl:1503.005]
dust: Dust scattering and extinction in the X-ray

Written in Python, dust calculates X-ray dust scattering and extinction in the intergalactic and local interstellar media.

[ascl:1503.004]
HELIOS-K: Opacity Calculator for Radiative Transfer

HELIOS-K is an opacity calculator for exoplanetary atmospheres. It takes a line list as an input and computes the line shapes of an arbitrary number of spectral lines (~millions to billions). HELIOS-K is capable of computing 100,000 spectral lines in 1 second; it is written in CUDA, is optimized for graphics processing units (GPUs), and can be used with the HELIOS radiative transfer code (ascl:1807.009).

[ascl:1503.003]
TAME: Tool for Automatic Measurement of Equivalent-width

TAME measures the equivalent width (EWs) in high-resolution spectra. Written by IDL, TAME provides the EWs of spectral lines by profile fitting in an automatic or interactive mode and is reliable for measuring EWs in a spectrum with a spectral resolution of R ≳ 20000. It offers an interactive mode for more flexible measurement of the EW and a fully automatic mode that can simultaneously measure the EWs for a large set of lines.

[ascl:1503.002]
Galax2d: 2D isothermal Euler equations solver

Galax2d computes the 2D stationary solution of the isothermal Euler equations of gas dynamics in a rotating galaxy with a weak bar. The gravitational potential represents a weak bar and controls the flow. A damped Newton method solves the second-order upwind discretization of the equations for a steady-state solution, using a consistent linearization and a direct solver. The code can be applied as a tool for generating flow models if used on not too fine meshes, up to 256 by 256 cells for half a disk in polar coordinates.

[ascl:1503.001]
K2flix: Kepler pixel data visualizer

K2flix makes it easy to inspect the CCD pixel data obtained by NASA's Kepler space telescope. The two-wheeled extended Kepler mission, K2, is affected by new sources of systematics, including pointing jitter and foreground asteroids, that are easier to spot by eye than by algorithm. The code takes Kepler's Target Pixel Files (TPF) as input and turns them into contrast-stretched animated gifs or MPEG-4 movies. K2flix can be used both as a command-line tool or using its Python API.

[ascl:1502.023]
ROBOSPECT: Width fitting program

ROBOSPECT, written in C, automatically measures and deblends line equivalent widths for absorption and emission spectra. ROBOSPECT should not be used for stars with spectra in which there is no discernible continuum over large wavelength regions, nor for the most carbon-enhanced stars for which spectral synthesis would be favored. Although ROBOSPECT was designed for metal-poor stars, it is capable of fitting absorption and emission features in a variety of astronomical sources.

[ascl:1502.022]
AstroLines: Astrophysical line list generator in the H-band

AstroLines adjusts spectral line parameters (gf and damping constant) starting from an initial line list. Written in IDL and tailored to the APO Galactic Evolution Experiment (APOGEE), it runs a slightly modified version of MOOG (ascl:1202.009) to compare synthetic spectra with FTS spectra of the Sun and Arcturus.

[ascl:1502.021]
MaLTPyNT: Quick look timing analysis for NuSTAR data

MaLTPyNT (Matteo's Libraries and Tools in Python for NuSTAR Timing) provides a quick-look timing analysis of NuSTAR data, properly treating orbital gaps and exploiting the presence of two independent detectors by using the cospectrum as a proxy for the power density spectrum. The output of the analysis is a cospectrum, or a power density spectrum, that can be fitted with XSPEC (ascl:9910.005) or ISIS (ascl:1302.002). The software also calculates time lags. Though written for NuSTAR data, MaLTPyNT can also perform standard spectral analysis on X-ray data from other satellite such as XMM-Newton and RXTE.

[ascl:1502.020]
ketu: Exoplanet candidate search code

ketu, written in Python, searches K2 light curves for evidence of exoplanets; the code simultaneously fits for systematic effects caused by small (few-pixel) drifts in the telescope pointing and other spacecraft issues and the transit signals of interest. Though more computationally expensive than standard search algorithms, it can be efficiently implemented and used to discover transit signals.

[ascl:1502.019]
XPCell: Convective plasma cells simulator

XPCell simulates convective plasma cells. The program is implemented in two versions, one using GNUPLOT and the second OpenGL. XPCell offers a GUI to introduce the parameter required by the program.

[ascl:1502.018]
XFGLENSES: Gravitational lens visualizer

XFGL visualizes gravitational lenses. It has an XFORM GUI and is completely interactive with the mouse. It uses OpenGL for the simulations.

[ascl:1502.017]
AMIsurvey: Calibration and imaging pipeline for radio data

AMIsurvey is a fully automated calibration and imaging pipeline for data from the AMI-LA radio observatory; it has two key dependencies. The first is drive-ami, included in this entry. Drive-ami is a Python interface to the specialized AMI-REDUCE calibration pipeline, which applies path delay corrections, automatic flags for interference, pointing errors, shadowing and hardware faults, applies phase and amplitude calibrations, Fourier transforms the data into the frequency domain, and writes out the resulting data in uvFITS format. The second is chimenea, which implements an automated imaging algorithm to convert the calibrated uvFITS into science-ready image maps. AMIsurvey links the calibration and imaging stages implemented within these packages together, configures the chimenea algorithm with parameters appropriate to data from AMI-LA, and provides a command-line interface.

[ascl:1502.016]
libnova: Celestial mechanics, astrometry and astrodynamics library

libnova is a general purpose, double precision, celestial mechanics, astrometry and astrodynamics library. Among many other calculations, it can calculate aberration, apparent position, proper motion, planetary positions, orbit velocities and lengths, angular separation of bodies, and hyperbolic motion of bodies.

[ascl:1502.015]
Camelus: Counts of Amplified Mass Elevations from Lensing with Ultrafast Simulations

Camelus provides a prediction on weak lensing peak counts from input cosmological parameters. Written in C, it samples halos from a mass function and assigns a profile, carries out ray-tracing simulations, and then counts peaks from ray-tracing maps. The creation of the ray-tracing simulations requires less computing time than N-body runs and the results is in good agreement with full N-body simulations.

[ascl:1502.014]
Magnetron: Fitting bursts from magnetars

Magnetron, written in Python, decomposes magnetar bursts into a superposition of small spike-like features with a simple functional form, where the number of model components is itself part of the inference problem. Markov Chain Monte Carlo (MCMC) sampling and reversible jumps between models with different numbers of parameters are used to characterize the posterior distributions of the model parameters and the number of components per burst.

[ascl:1502.013]
Rabacus: Analytic Cosmological Radiative Transfer Calculations

Rabacus performs analytic radiative transfer calculations in simple geometries relevant to cosmology and astrophysics; it also contains tools to calculate cosmological quantities such as the power spectrum and mass function. With core routines written in Fortran 90 and then wrapped in Python, the execution speed is thousands of times faster than equivalent routines written in pure Python.

[ascl:1502.012]
SPHGR: Smoothed-Particle Hydrodynamics Galaxy Reduction

SPHGR (Smoothed-Particle Hydrodynamics Galaxy Reduction) is a python based open-source framework for analyzing smoothed-particle hydrodynamic simulations. Its basic form can run a baryonic group finder to identify galaxies and a halo finder to identify dark matter halos; it can also assign said galaxies to their respective halos, calculate halo & galaxy global properties, and iterate through previous time steps to identify the most-massive progenitors of each halo and galaxy. Data about each individual halo and galaxy is collated and easy to access.

SPHGR supports a wide range of simulations types including N-body, full cosmological volumes, and zoom-in runs. Support for multiple SPH code outputs is provided by pyGadgetReader (ascl:1411.001), mainly Gadget (ascl:0003.001) and TIPSY (ascl:1111.015).

[ascl:1502.011]
PolyChord: Nested sampling for cosmology

PolyChord is a Bayesian inference tool for the simultaneous calculation of evidences and sampling of posterior distributions. It is a variation on John Skilling's Nested Sampling, utilizing Slice Sampling to generate new live points. It performs well on moderately high dimensional (~100s D) posterior distributions, and can cope with arbitrary degeneracies and multimodality.

[ascl:1502.010]
nbody6tt: Tidal tensors in N-body simulations

nbody6tt, based on Aarseth's nbody6 (ascl:1102.006) code, includes the treatment of complex galactic tides in a direct N-body simulation of a star cluster through the use of tidal tensors (tt) and offers two complementary methods. The first allows consideration of any kind of galaxy and orbit, thus offering versatility; this method cannot be used to study tidal debris, as it relies on the tidal approximation (linearization of the tidal force). The second method is not limited by this and does not require a galaxy simulation; the user defines a numerical function which takes position and time as arguments, and the galactic potential is returned. The space and time derivatives of the potential are used to (i) integrate the motion of the cluster on its orbit in the galaxy (starting from user-defined initial position and velocity vector), and (ii) compute the tidal acceleration on the stars.

[ascl:1502.009]
HDS: Hierarchical Data System

Pearce, Dave; Walter, Anton; Lupton, W. F.; Warren-Smith, Rodney F.; Lawden, Mike; McIlwrath, Brian; Peden, J. C. M.; Jenness, Tim; Draper, Peter W.

The Hierarchical Data System (HDS) is a file-based hierarchical data system designed for the storage of a wide variety of information. It is particularly suited to the storage of large multi-dimensional arrays (with their ancillary data) where efficient access is needed. It is a key component of the Starlink software collection (ascl:1110.012) and is used by the Starlink N-Dimensional Data Format (NDF) library (ascl:1411.023).

HDS organizes data into hierarchies, broadly similar to the directory structure of a hierarchical filing system, but contained within a single HDS container file. The structures stored in these files are self-describing and flexible; HDS supports modification and extension of structures previously created, as well as functions such as deletion, copying, and renaming. All information stored in HDS files is portable between the machines on which HDS is implemented. Thus, there are no format conversion problems when moving between machines. HDS can write files in a private binary format (version 4), or be layered on top of HDF5 (version 5).

[ascl:1502.008]
KAPPA: Optically thin spectra synthesis for non-Maxwellian kappa-distributions

Based on the freely available CHIANTI (ascl:9911.004) database and software, KAPPA synthesizes line and continuum spectra from the optically thin spectra that arise from collisionally dominated astrophysical plasmas that are the result of non-Maxwellian κ-distributions detected in the solar transition region and flares. Ionization and recombination rates together with the ionization equilibria are provided for a range of κ values. Distribution-averaged collision strengths for excitation are obtained by an approximate method for all transitions in all ions available within CHIANTI; KAPPA also offers tools for calculating synthetic line and continuum intensities.

[ascl:1502.007]
PyBDSF: Python Blob Detection and Source Finder

PyBDSF (Python Blob Detector and Source Finder, formerly PyBDSM) decomposes radio interferometry images into sources and makes their properties available for further use. PyBDSF can decompose an image into a set of Gaussians, shapelets, or wavelets as well as calculate spectral indices and polarization properties of sources and measure the psf variation across an image. PyBDSF uses an interactive environment based on CASA (ascl:1107.013); PyBDSF may also be used in Python scripts.

[ascl:1502.006]
Montblanc: GPU accelerated Radio Interferometer Measurement Equations in support of Bayesian Inference for Radio Observations

Montblanc, written in Python, is a GPU implementation of the Radio interferometer measurement equation (RIME) in support of the Bayesian inference for radio observations (BIRO) technique. The parameter space that BIRO explores results in tens of thousands of computationally expensive RIME evaluations before reduction to a single *X ^{2}* value. The RIME is calculated over four dimensions, time, baseline, channel and source and the values in this 4D space can be independently calculated; therefore, the RIME is particularly amenable to a parallel implementation accelerated by Graphics Programming Units (GPUs). Montblanc is implemented for NVIDIA's CUDA architecture and outperforms MeqTrees (ascl:1209.010) and OSKAR.

[ascl:1502.005]
PARSEC: PARametrized Simulation Engine for Cosmic rays

PARSEC (PARametrized Simulation Engine for Cosmic rays) is a simulation engine for fast generation of ultra-high energy cosmic ray data based on parameterizations of common assumptions of UHECR origin and propagation. Implemented are deflections in unstructured turbulent extragalactic fields, energy losses for protons due to photo-pion production and electron-pair production, as well as effects from the expansion of the universe. Additionally, a simple model to estimate propagation effects from iron nuclei is included. Deflections in the Galactic magnetic field are included using a matrix approach with precalculated lenses generated from backtracked cosmic rays. The PARSEC program is based on object oriented programming paradigms enabling users to extend the implemented models and is steerable with a graphical user interface.

[ascl:1502.004]
ADAM: All-Data Asteroid Modeling

ADAM (All-Data Asteroid Modeling) models asteroid shape reconstruction from observations. Developed in MATLAB with core routines in C, its features include general nonconvex and non-starlike parametric 3D shape supports and reconstruction of asteroid shape from any combination of lightcurves, adaptive optics images, HST/FGS data, disk-resolved thermal images, interferometry, and range-Doppler radar images. ADAM does not require boundary contour extraction for reconstruction and can be run in parallel.

[ascl:1502.003]
N-GenIC: Cosmological structure initial conditions

N-GenIC is an initial conditions code for cosmological structure formation that can be used to set-up random N-body realizations of Gaussian random fields with a prescribed power spectrum in a homogeneously sampled periodic box. The code creates cosmological initial conditions based on the Zeldovich approximation, in a format directly compatible with GADGET or AREPO.

[ascl:1502.002]
OpenOrb: Open-source asteroid orbit computation software

OpenOrb (OOrb) contains tools for rigorously estimating the uncertainties resulting from the inverse problem of computing orbital elements using scarce astrometry. It uses the least-squares method and also contains both Monte-Carlo (MC) and Markov-Chain MC versions of the statistical ranging method. Ranging obtains sampled, non-Gaussian orbital-element probability-density functions and is optimized for cases where the amount of astrometry is scarce or spans a relatively short time interval.

[ascl:1502.001]
RH 1.5D: Polarized multi-level radiative transfer with partial frequency distribution

RH 1.5D performs Zeeman multi-level non-local thermodynamical equilibrium calculations with partial frequency redistribution for an arbitrary amount of chemical species. Derived from the RH code and written in C, it calculates spectra from 3D, 2D or 1D atmospheric models on a column-by-column basis (or 1.5D). It includes optimization features to speed up or improve convergence, which are particularly useful in dynamic models of chromospheres. While one should be aware of its limitations, the calculation of spectra using the 1.5D or column-by-column is a good approximation in many cases, and generally allows for faster convergence and more flexible methods of improving convergence. RH 1.5D scales well to at least tens of thousands of CPU cores.

[ascl:1501.016]
Colossus: COsmology, haLO, and large-Scale StrUcture toolS

Colossus is a collection of Python modules for cosmology and dark matter halos calculations. It performs cosmological calculations with an emphasis on structure formation applications, implements general and specific density profiles, and provides a large range of models for the concentration-mass relation, including a conversion to arbitrary mass definitions.

[ascl:1501.015]
Exoplanet: Trans-dimensional MCMC method for exoplanet discovery

Exoplanet determines the posterior distribution of exoplanets by use of a trans-dimensional Markov Chain Monte Carlo method within Nested Sampling. This method finds the posterior distribution in a single run rather than requiring multiple runs with trial values.

[ascl:1501.014]
GalPaK 3D: Galaxy parameters and kinematics extraction from 3D data

GalPaK 3D extracts the intrinsic (i.e. deconvolved) galaxy parameters and kinematics from any 3-dimensional data. The algorithm uses a disk parametric model with 10 free parameters (which can also be fixed independently) and a MCMC approach with non-traditional sampling laws in order to efficiently probe the parameter space. More importantly, it uses the knowledge of the 3-dimensional spread-function to return the intrinsic galaxy properties and the intrinsic data-cube. The 3D spread-function class is flexible enough to handle any instrument.

GalPaK 3D can simultaneously constrain the kinematics and morphological parameters of (non-merging, i.e. regular) galaxies observed in non-optimal seeing conditions and can also be used on AO data or on high-quality, high-SNR data to look for non-axisymmetric structures in the residuals.

[ascl:1501.013]
Molecfit: Telluric absorption correction tool

Smette, A.; Kausch, W; Sana, H; Noll, S.; Horst, H.; Kimeswenger, S.; Barden, M; Szyszka, C.; Jones, A. M.; Gallene, A.; Vinther, J.; Ballester, P.; Kerber, F.

Molecfit corrects astronomical observations for atmospheric absorption features based on fitting synthetic transmission spectra to the astronomical data, which saves a significant amount of valuable telescope time and increases the instrumental efficiency. Molecfit can also estimate molecular abundances, especially the water vapor content of the Earth’s atmosphere. The tool can be run from a command-line or more conveniently through a GUI.

[ascl:1501.012]
Exorings: Exoring modelling software

Exorings, written in Python, contains tools for displaying and fitting giant extrasolar planet ring systems; it uses FITS formatted data for input.

[ascl:1501.011]
transfer: The Sloan Digital Sky Survey Data Transfer Infrastructure

The Sloan Digital Sky Survey (SDSS) produces large amounts of data daily. transfer, written in Python, provides the effective automation needed for daily data transfer operations and management and operates essentially free of human intervention. This package has been tested and used successfully for several years.

[ascl:1501.010]
PythonPhot: Simple DAOPHOT-type photometry in Python

PythonPhot is a simple Python translation of DAOPHOT-type (ascl:1104.011) photometry procedures from the IDL AstroLib (Landsman 1993), including aperture and PSF-fitting algorithms, with a few modest additions to increase functionality and ease of use. These codes allow fast, easy, and reliable photometric measurements and are currently used in the Pan-STARRS supernova pipeline and the HST CLASH/CANDELS supernova analysis.

[ascl:1501.009]
BIANCHI: Bianchi VIIh Simulations

BIANCHI provides functionality to support the simulation of Bianchi Type VIIh induced temperature fluctuations in CMB maps of a universe with shear and rotation. The implementation is based on the solutions to the Bianchi models derived by Barrow et al. (1985), which do not incorporate any dark energy component. Functionality is provided to compute the induced fluctuations on the sphere directly in either real or harmonic space.

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