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[ascl:1603.004] gPhoton: Time-tagged GALEX photon events analysis tools

Written in Python, gPhoton calibrates and sky-projects the ~1.1 trillion ultraviolet photon events detected by the microchannel plates on the Galaxy Evolution Explorer Spacecraft (GALEX), archives these events in a publicly accessible database at the Mikulski Archive for Space Telescopes (MAST), and provides tools for working with the database to extract scientific results, particularly over short time domains. The software includes a re-implementation of core functionality of the GALEX mission calibration pipeline to produce photon list files from raw spacecraft data as well as a suite of command line tools to generate calibrated light curves, images, and movies from the MAST database.

[ascl:1603.003] VIP: Vortex Image Processing pipeline for high-contrast direct imaging of exoplanets

VIP (Vortex Image Processing pipeline) provides pre- and post-processing algorithms for high-contrast direct imaging of exoplanets. Written in Python, VIP provides a very flexible framework for data exploration and image processing and supports high-contrast imaging observational techniques, including angular, reference-star and multi-spectral differential imaging. Several post-processing algorithms for PSF subtraction based on principal component analysis are available as well as the LLSG (Local Low-rank plus Sparse plus Gaussian-noise decomposition) algorithm for angular differential imaging. VIP also implements the negative fake companion technique coupled with MCMC sampling for rigorous estimation of the flux and position of potential companions.

[ascl:1603.002] CORBITS: Efficient Geometric Probabilities of Multi-Transiting Exoplanetary Systems

CORBITS (Computed Occurrence of Revolving Bodies for the Investigation of Transiting Systems) computes the probability that any particular group of exoplanets can be observed to transit from a collection of conjectured exoplanets orbiting a star. The efficient, semi-analytical code computes the areas bounded by circular curves on the surface of a sphere by applying elementary differential geometry. CORBITS is faster than previous algorithms, based on comparisons with Monte Carlo simulations, and tests show that it is extremely accurate even for highly eccentric planets.

[ascl:1603.001] SILSS: SPHERE/IRDIS Long-Slit Spectroscopy pipeline

The ESO's VLT/SPHERE instrument includes a unique long-slit spectroscopy (LSS) mode coupled with Lyot coronagraphy in its infrared dual-band imager and spectrograph (IRDIS) for spectral characterization of young, giant exoplanets detected by direct imaging. The SILSS pipeline is a combination of the official SPHERE pipeline and additional custom IDL routines developed within the SPHERE consortium for the speckle subtraction and spectral extraction of a companion's spectrum; it offers a complete end-to-end pipeline, from raw data (science+calibrations) to a final spectrum of the companion. SILSS works on both the low-resolution (LRS) and medium-resolution (MRS) data, and allows correction for some of the known biases of the instrument. Documentation is included in the header of the main routine of the pipeline.

[ascl:1602.021] COLAcode: COmoving Lagrangian Acceleration code

COLAcode is a serial particle mesh-based N-body code illustrating the COLA (COmoving Lagrangian Acceleration) method; it solves for Large Scale Structure (LSS) in a frame that is comoving with observers following trajectories calculated in Lagrangian Perturbation Theory (LPT). It differs from standard N-body code by trading accuracy at small-scales to gain computational speed without sacrificing accuracy at large scales. This is useful for generating large ensembles of accurate mock halo catalogs required to study galaxy clustering and weak lensing; such catalogs are needed to perform detailed error analysis for ongoing and future surveys of LSS.

[ascl:1602.020] mbb_emcee: Modified Blackbody MCMC

Mbb_emcee fits modified blackbodies to photometry data using an affine invariant MCMC. It has large number of options which, for example, allow computation of the IR luminosity or dustmass as part of the fit. Carrying out a fit produces a HDF5 output file containing the results, which can either be read directly, or read back into a mbb_results object for analysis. Upper and lower limits can be imposed as well as Gaussian priors on the model parameters. These additions are useful for analyzing poorly constrained data. In addition to standard Python packages scipy, numpy, and cython, mbb_emcee requires emcee (ascl:1303.002), Astropy (ascl:1304.002), h5py, and for unit tests, nose.

[ascl:1602.019] CLOC: Cluster Luminosity Order-Statistic Code

CLOC computes cluster order statistics, i.e. the luminosity distribution of the Nth most luminous cluster in a population. It is flexible and requires few assumptions, allowing for parametrized variations in the initial cluster mass function and its upper and lower cutoffs, variations in the cluster age distribution, stellar evolution and dust extinction, as well as observational uncertainties in both the properties of star clusters and their underlying host galaxies. It uses Markov chain Monte Carlo methods to search parameter space to find best-fitting values for the parameters describing cluster formation and disruption, and to obtain rigorous confidence intervals on the inferred values.

[ascl:1602.018] POPPY: Physical Optics Propagation in PYthon

POPPY (Physical Optics Propagation in PYthon) simulates physical optical propagation including diffraction. It implements a flexible framework for modeling Fraunhofer and Fresnel diffraction and point spread function formation, particularly in the context of astronomical telescopes. POPPY provides the optical modeling framework for WebbPSF (ascl:1504.007) and was developed as part of a simulation package for JWST, but is available separately and is broadly applicable to many kinds of imaging simulations.

[ascl:1602.017] CHIP: Caltech High-res IRS Pipeline

CHIP (Caltech High-res IRS Pipeline) reduces high signal-to-noise short-high and long-high Spitzer-IRS spectra, especially that taken with dedicated background exposures. Written in IDL, it is independent of other Spitzer reduction tools except IRSFRINGE (ascl:1602.016).

[ascl:1602.016] IRSFRINGE: Interactive tool for fringe removal from Spitzer IRS spectra

IRSFRINGE is an IDL-based GUI package that allows observers to interactively remove fringes from IRS spectra. Fringes that originate from the detector subtrates are observed in the IRS Short-High (SH) and Long-High (LH) modules. In the Long-Low (LL) module, another fringe component is seen as a result of the pre-launch change in one of the LL filters. The fringes in the Short-Low (SL) module are not spectrally resolved. the fringes are already largely removed in the pipeline processing when the flat field is applied. However, this correction is not perfect and remaining fringes can be removed with IRSFRINGE from data in each module. IRSFRINGE is available as a stand-alone package and is also part of the Spectroscopic Modeling, Analysis and Reduction Tool (SMART, ascl:1210.021).

[ascl:1602.015] GANDALF: Graphical Astrophysics code for N-body Dynamics And Lagrangian Fluids

GANDALF, a successor to SEREN (ascl:1102.010), is a hybrid self-gravitating fluid dynamics and collisional N-body code primarily designed for investigating star formation and planet formation problems. GANDALF uses various implementations of Smoothed Particle Hydrodynamics (SPH) to perform hydrodynamical simulations of gas clouds undergoing gravitational collapse to form new stars (or other objects), and can perform simulations of pure N-body dynamics using high accuracy N-body integrators, model the intermediate phase of cluster evolution, and provide visualizations via its python interface as well as interactive simulations. Although based on many of the SEREN routines, GANDALF has been largely re-written from scratch in C++ using more optimal algorithms and data structures.

[ascl:1602.014] k2photometry: Read, reduce and detrend K2 photometry

k2photometry reads, reduces and detrends K2 photometry and searches for transiting planets. MAST database pixel files are used as input; the output includes raw lightcurves, detrended lightcurves and a transit search can be performed as well. Stellar variability is not typically well-preserved but parameters can be tweaked to change that. The BLS algorithm used to detect periodic events is a Python implementation by Ruth Angus and Dan Foreman-Mackey (https://github.com/dfm/python-bls).

[ascl:1602.013] TailZ: Redshift distributions estimator of photometric samples of galaxies

TailZ estimates redshift distributions of photometric samples of galaxies selected photometrically given a subsample with measured spectroscopic redshifts. The approach uses a non-parametric Voronoi tessellation density estimator to interpolate the galaxy distribution in the redshift and photometric color space. The Voronoi tessellation estimator performs well at reconstructing the tails of the redshift distribution of individual galaxies and gives unbiased estimates of the first and second moments.

[ascl:1602.012] DELightcurveSimulation: Light curve simulation code

DELightcurveSimulation (also called DELCgen) simulates light curves with any given power spectral density and any probability density function, following the algorithm described in Emmanoulopoulos et al. (2013). The simulated products have exactly the same variability and statistical properties as the observed light curves. The code is a Python implementation of the Mathematica code provided by Emmanoulopoulos et al.

[ascl:1602.011] Celestial: Common astronomical conversion routines and functions

The R package Celestial contains common astronomy conversion routines, particularly the HMS and degrees schemes, and a large range of functions for calculating properties of different cosmologies (as used by the cosmocalc website). This includes distances, ages, growth rate/factor and densities (e.g., Omega evolution and critical energy density). It also includes functions for calculating thermal properties of the CMB and Planck's equations and virial properties of halos in different cosmologies, and standard NFW and weak-lensing formulas and low level orbital routines for calculating Roche properties, Vis-Viva and free-fall times.

[ascl:1602.010] The Cannon: Data-driven method for determining stellar parameters and abundances from stellar spectra

The Cannon is a data-driven method for determining stellar labels (physical parameters and chemical abundances) from stellar spectra in the context of vast spectroscopic surveys. It fits for the spectral model given training spectra and labels, with the polynomial order for the spectral model decided by the user, infers labels for the test spectra, and provides diagnostic output for monitoring and evaluating the process. It offers SNR-independent continuum normalization, performs well at lower signal-to-noise, and is very accurate.

[ascl:1602.009] LensTools: Weak Lensing computing tools

LensTools implements a wide range of routines frequently used in Weak Gravitational Lensing, including tools for image analysis, statistical processing and numerical theory predictions. The package offers many useful features, including complete flexibility and easy customization of input/output formats; efficient measurements of power spectrum, PDF, Minkowski functionals and peak counts of convergence maps; survey masks; artificial noise generation engines; easy to compute parameter statistical inferences; ray tracing simulations; and many others. It requires standard numpy and scipy, and depending on tools used, may require Astropy (ascl:1304.002), emcee (ascl:1303.002), matplotlib, and mpi4py.

[ascl:1602.008] NuCraft: Oscillation probabilities for atmospheric neutrinos calculator

NuCraft calculates oscillation probabilities for atmospheric neutrinos, taking into account matter effects and the Earth's atmosphere, and supports an arbitrary number of sterile neutrino flavors with easily configurable continuous Earth models. Continuous modeling of the Earth instead of the often-used approximation of four layers with constant density and consideration of the smearing of baseline lengths due to the variable neutrino production heights in Earth's atmosphere each lead to deviations of 10% or more for conventional neutrinos between 1 and 10 GeV.

[ascl:1602.007] FilTER: Filament Trait-Evaluated Reconstruction

FilTER (Filament Trait-Evaluated Reconstruction) post-processes output from DisPerSE (ascl:1302.015 ) to produce a set of filaments that are well-defined and have measured properties (e.g. width), then cuts the profiles, fits and assesses them to reconstruct new filaments according to defined criteria.

[ascl:1602.006] LIRA: LInear Regression in Astronomy

LIRA (LInear Regression in Astronomy) performs Bayesian linear regression that accounts for heteroscedastic errors in both the independent and the dependent variables, intrinsic scatters (in both variables), time evolution of slopes, normalization and scatters, Malmquist and Eddington bias, and break of linearity. The posterior distribution of the regression parameters is sampled with a Gibbs method exploiting the JAGS (ascl:1209.002) library.

[ascl:1602.005] LRGS: Linear Regression by Gibbs Sampling

LRGS (Linear Regression by Gibbs Sampling) implements a Gibbs sampler to solve the problem of multivariate linear regression with uncertainties in all measured quantities and intrinsic scatter. LRGS extends an algorithm by Kelly (2007) that used Gibbs sampling for performing linear regression in fairly general cases in two ways: generalizing the procedure for multiple response variables, and modeling the prior distribution of covariates using a Dirichlet process.

[ascl:1602.004] DUSTYWAVE: Linear waves in gas and dust

Written in Fortran, DUSTYWAVE computes the exact solution for linear waves in a two-fluid mixture of gas and dust. The solutions are general with respect to both the dust-to-gas ratio and the amplitude of the drag coefficient.

[ascl:1602.003] ZAP: Zurich Atmosphere Purge

ZAP (Zurich Atmosphere Purge) provides sky subtraction for integral field spectroscopy; its approach is based on principal component analysis (PCA) developed for the Multi Unit Spectrographic Explorer (MUSE) integral field spectrograph. ZAP employs filtering and data segmentation to enhance the inherent capabilities of PCA for sky subtraction. ZAP reduces sky emission residuals while robustly preserving the flux and line shapes of astronomical sources; this method works in a variety of observational situations from sparse fields with a low density of sources to filled fields in which the target source fills the field of view. With the inclusion of both of these situations the method is generally applicable to many different science cases and should also be useful for other instrumentation.

[ascl:1602.002] pyraf-dbsp: Reduction pipeline for the Palomar Double Beam Spectrograph

pyraf-dbsp is a PyRAF-based (ascl:1207.011) reduction pipeline for optical spectra taken with the Palomar 200-inch Double Beam Spectrograph. The pipeline provides a simplified interface for basic reduction of single-object spectra with minimal overhead. It is suitable for quicklook classification of transients as well as moderate-precision (few km/s) radial velocity work.

[ascl:1602.001] Automark: Automatic marking of marked Poisson process in astronomical high-dimensional datasets

Automark models photon counts collected form observation of variable-intensity astronomical sources. It aims to mark the abrupt changes in the corresponding wavelength distribution of the emission automatically. In the underlying methodology, change points are embedded into a marked Poisson process, where photon wavelengths are regarded as marks and both the Poisson intensity parameter and the distribution of the marks are allowed to change.

[ascl:1601.021] ISO: Isochrone construction

ISO transforms MESA history files into a uniform basis for interpolation and then constructs new stellar evolution tracks and isochrones from that basis. It is written in Fortran and requires MESA (ascl:1010.083), primarily for interpolation. Though designed to ingest MESA star history files, tracks from other stellar evolution codes can be incorporated by loading the tracks into the data structures used in the codes.

[ascl:1601.020] ProC: Process Coordinator

ProC (short for Process Coordinator) is a versatile workflow engine that allows the user to build, run and manage workflows with just a few clicks. It automatically documents every processing step, making every modification to data reproducible. ProC provides a graphical user interface for constructing complex data processing workflows out of a given set of computer programs. The user can, for example, specify that only data products which are affected by a change in the input data are updated selectively, avoiding unnecessary computations. The ProC suite is flexible and satisfies basic needs of data processing centers that have to be able to restructure their data processing along with the development of a project.

[ascl:1601.019] WzBinned: Binned and uncorrelated estimates of dark energy EOS extractor

WzBinned extracts binned and uncorrelated estimates of dark energy equation of state w(z) using Type Ia supernovae Hubble diagram and other cosmological probes and priors. It can handle an arbitrary number of input distance modulus data (entered as an input file SNdata.dat) and various existing cosmological information.

[ascl:1601.018] MATPHOT: Stellar photometry and astrometry with discrete point spread functions

A discrete Point Spread Function (PSF) is a sampled version of a continuous two-dimensional PSF. The shape information about the photon scattering pattern of a discrete PSF is typically encoded using a numerical table (matrix) or a FITS image file. MATPHOT shifts discrete PSFs within an observational model using a 21-pixel- wide damped sinc function and position partial derivatives are computed using a five-point numerical differentiation formula. MATPHOT achieves accurate and precise stellar photometry and astrometry of undersampled CCD observations by using supersampled discrete PSFs that are sampled two, three, or more times more finely than the observational data.

[ascl:1601.017] BASCS: Bayesian Separation of Close Sources

BASCS models spatial and spectral information from overlapping sources and the background, and jointly estimates all individual source parameters. The use of spectral information improves the detection of both faint and closely overlapping sources and increases the accuracy with which source parameters are inferred.

[ascl:1601.016] Fit Kinematic PA: Fit the global kinematic position-angle of galaxies

Fit kinematic PA measures the global kinematic position-angle (PA) from integral field observations of a galaxy stellar or gas kinematics; the code is available in IDL and Python.

[ascl:1601.015] QDPHOT: Quick & Dirty PHOTometry

QDPHOT is a fast CCD stellar photometry task which quickly produces CCD stellar photometry from two CCD images of a star field. It was designed to be a data mining tool for finding high-quality stellar observations in the data archives of the National Virtual Observatory. QDPHOT typically takes just a few seconds to analyze two Hubble Space Telescope WFPC2 observations of Local Group star clusters. It is also suitable for real-time data-quality analysis of CCD observations; on-the-fly instrumental color-magnitude diagrams can be produced at the telescope console during the few seconds between CCD readouts.

[ascl:1601.014] Nulike: Neutrino telescope likelihood tools

Nulike is software for including full event-level information in likelihood calculations for neutrino telescope searches for dark matter annihilation. It includes both angular and spectral information about neutrino events as well as their total number, and can be used for single models without reference to the rest of a parameter space.

[ascl:1601.013] ImpactModel: Black Hole Accretion Disk Impact Model

ImpactModel, written in Cython, computes the accretion disc impact spectrum at given frequencies and can compute other model quantities as a function of time.

[ascl:1601.012] SavGolFilterCov: Savitzky Golay filter for data with error covariance

A Savitzky–Golay filter is often applied to data to smooth the data without greatly distorting the signal; however, almost all data inherently comes with noise, and the noise properties can differ from point to point. This python script improves upon the traditional Savitzky-Golay filter by accounting for error covariance in the data. The inputs and arguments are modeled after scipy.signal.savgol_filter.

[ascl:1601.011] LACEwING: LocAting Constituent mEmbers In Nearby Groups

LACEwING (LocAting Constituent mEmbers In Nearby Groups) uses the kinematics (positions and motions) of stars to determine if they are members of one of 10 nearby young moving groups or 4 nearby open clusters within 100 parsecs. It is written for Python 2.7 and depends upon Numpy, Scipy, and Astropy (ascl:1304.002) modules. LACEwING can be used as a stand-alone code or as a module in other code. Additional python programs are present in the repository for the purpose of recalibrating the code and producing other analyses, including a traceback analysis.

[ascl:1601.010] PARAVT: Parallel Voronoi Tessellation

PARAVT offers massive parallel computation of Voronoi tessellations (VT hereafter) in large data sets. The code is focused for astrophysical purposes where VT densities and neighbors are widely used. There are several serial Voronoi tessellation codes, however no open source and parallel implementations are available to handle the large number of particles/galaxies in current N-body simulations and sky surveys. Parallelization is implemented under MPI and VT using Qhull library. Domain decomposition take into account consistent boundary computation between tasks, and support periodic conditions. In addition, the code compute neighbors lists, Voronoi density and Voronoi cell volumes for each particle, and can compute density on a regular grid.

[ascl:1601.009] K2fov: Field of view software for NASA's K2 mission

K2fov allows users to transform celestial coordinates into K2's pixel coordinate system for the purpose of preparing target proposals and field of view visualizations. In particular, the package, written in Python, adds the "K2onSilicon" and "K2findCampaigns" tools to the command line, allowing the visibility of targets to be checked in a user-friendly way.

[ascl:1601.008] CosmicPy: Interactive cosmology computations

CosmicPy performs simple and interactive cosmology computations for forecasting cosmological parameters constraints; it computes tomographic and 3D Spherical Fourier-Bessel power spectra as well as Fisher matrices for galaxy clustering. Written in Python, it relies on a fast C++ implementation of Fourier-Bessel related computations, and requires NumPy, SciPy, and Matplotlib.

[ascl:1601.007] LIRA: Low-counts Image Reconstruction and Analysis

LIRA (Low-counts Image Reconstruction and Analysis) deconvolves any unknown sky components, provides a fully Poisson 'goodness-of-fit' for any best-fit model, and quantifies uncertainties on the existence and shape of unknown sky. It does this without resorting to χ2 or rebinning, which can lose high-resolution information. It is written in R and requires the FITSio package.

[ascl:1601.006] SAGE: Semi-Analytic Galaxy Evolution

SAGE (Semi-Analytic Galaxy Evolution) models galaxy formation in a cosmological context. SAGE has been rebuilt to be modular and customizable. The model runs on any dark matter cosmological N-body simulation whose trees are organized in a supported format and contain a minimum set of basic halo properties.

[ascl:1601.005] ctools: Cherenkov Telescope Science Analysis Software

ctools provides tools for the scientific analysis of Cherenkov Telescope Array (CTA) data. Analysis of data from existing Imaging Air Cherenkov Telescopes (such as H.E.S.S., MAGIC or VERITAS) is also supported, provided that the data and response functions are available in the format defined for CTA. ctools comprises a set of ftools-like binary executables with a command-line interface allowing for interactive step-wise data analysis. A Python module allows control of all executables, and the creation of shell or Python scripts and pipelines is supported. ctools provides cscripts, which are Python scripts complementing the binary executables. Extensions of the ctools package by user defined binary executables or Python scripts is supported. ctools are based on GammaLib (ascl:1110.007).

[ascl:1601.004] Odyssey: Ray tracing and radiative transfer in Kerr spacetime

Odyssey is a GPU-based General Relativistic Radiative Transfer (GRRT) code for computing images and/or spectra in Kerr metric describing the spacetime around a rotating black hole. Odyssey is implemented in CUDA C/C++. For flexibility, the namespace structure in C++ is used for different tasks; the two default tasks presented in the source code are the redshift of a Keplerian disk and the image of a Keplerian rotating shell at 340GHz. Odyssey_Edu, an educational software package for visualizing the ray trajectories in the Kerr spacetime that uses Odyssey, is also available.

[ascl:1601.003] SCOUSE: Semi-automated multi-COmponent Universal Spectral-line fitting Engine

The Semi-automated multi-COmponent Universal Spectral-line fitting Engine (SCOUSE) is a spectral line fitting algorithm that fits Gaussian files to spectral line emission. It identifies the spatial area over which to fit the data and generates a grid of spectral averaging areas (SAAs). The spatially averaged spectra are fitted according to user-provided tolerance levels, and the best fit is selected using the Akaike Information Criterion, which weights the chisq of a best-fitting solution according to the number of free-parameters. A more detailed inspection of the spectra can be performed to improve the fit through an iterative process, after which SCOUSE integrates the new solutions into the solution file.

[ascl:1601.002] Hyper-Fit: Fitting routines for multidimensional data with multivariate Gaussian uncertainties

The R package Hyper-Fit fits hyperplanes (hyper.fit) and creates 2D/3D visualizations (hyper.plot2d / hyper.plot3d) to produce robust 1D linear fits for 2D x vs y type data, and robust 2D plane fits to 3D x vs y vs z type data. This hyperplane fitting works generically for any N-1 hyperplane model being fit to a N dimensional dataset. All fits include intrinsic scatter in the generative model orthogonal to the hyperplane. A web interface for online fitting is also available at http://hyperfit.icrar.org.

[ascl:1601.001] TRADES: TRAnsits and Dynamics of Exoplanetary Systems

TRADES (TRAnsits and Dynamics of Exoplanetary Systems) simultaneously fits observed radial velocities and transit times data to determine the orbital parameters of exoplanetary systems from observational data. It uses a dynamical simulator for N-body systems that also fits the available data during the orbital integration and determines the best combination of the orbital parameters using grid search, χ2 minimization, genetic algorithms, particle swarm optimization, and bootstrap analysis.

[submitted] pyreaclib

A python interface to the JINA reaclib nuclear reaction database

[ascl:1512.020] TACT: The Action Computation Tool

The Action Computation Tool (TACT) tests methods for estimating actions, angles and frequencies of orbits in both axisymmetric and triaxial potentials, including general spherical potentials, analytic potentials (Isochrone and Harmonic oscillator), axisymmetric Stackel fudge, average generating function from orbit (AvGF), and others. It is written in C++; code is provided to compile the routines into a Python library. TM (ascl:1512.014) and LAPACK are required to access some features.

[ascl:1512.019] UPSILoN: AUtomated Classification of Periodic Variable Stars using MachIne LearNing

UPSILoN (AUtomated Classification of Periodic Variable Stars using MachIne LearNing) classifies periodic variable stars such as Delta Scuti stars, RR Lyraes, Cepheids, Type II Cepheids, eclipsing binaries, and long-period variables (i.e. superclasses), and their subclasses (e.g. RR Lyrae ab, c, d, and e types) using well-sampled light curves from any astronomical time-series surveys in optical bands regardless of their survey-specific characteristics such as color, magnitude, and sampling rate. UPSILoN consists of two parts, one which extracts variability features from a light curve, and another which classifies a light curve, and returns extracted features, a predicted class, and a class probability. In principle, UPSILoN can classify any light curves having arbitrary number of data points, but using light curves with more than ~80 data points provides the best classification quality.

[ascl:1512.018] growl: Growth factor and growth rate of expanding universes

Growl calculates the linear growth factor Da and its logarithmic derivative dln D/dln a in expanding Friedmann-Robertson-Walker universes with arbitrary matter and vacuum densities. It permits rapid and stable numerical evaluation.

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