The "busy function" accurately describes the characteristic double-horn HI profile of many galaxies. Implemented in a C/C++ library and Python module called BF_dist, it is a continuous, differentiable function that consists of only two basic functions, the error function, erf(x), and a polynomial, |x|^n, of degree n >= 2. BF_dist offers great flexibility in fitting a wide range of HI profiles from the Gaussian profiles of dwarf galaxies to the broad, asymmetric double-horn profiles of spiral galaxies, and can be used to parametrize observed HI spectra of galaxies and the construction of spectral templates for simulations and matched filtering algorithms accurately and efficiently.

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 https://hyperfit.icrar.org.

pydftools is a pure-python port of the dftools R package (ascl:1805.002), which finds the most likely P parameters of a D-dimensional distribution function (DF) generating N objects, where each object is specified by D observables with measurement uncertainties. For instance, if the objects are galaxies, it can fit a MF (P=1), a mass-size distribution (P=2) or the mass-spin-morphology distribution (P=3). Unlike most common fitting approaches, this method accurately accounts for measurement in uncertainties and complex selection functions. Though this package imitates the dftools package quite closely while being as Pythonic as possible, it has not implemented 2D+ nor non-parametric.

dftools, written in R, finds the most likely P parameters of a D-dimensional distribution function (DF) generating N objects, where each object is specified by D observables with measurement uncertainties. For instance, if the objects are galaxies, it can fit a mass function (D=1), a mass-size distribution (D=2) or the mass-spin-morphology distribution (D=3). Unlike most common fitting approaches, this method accurately accounts for measurement in uncertainties and complex selection functions.

Shark is a flexible semi-analytic galaxy formation model for easy exploration of different physical processes. Shark has been implemented with several models for gas cooling, active galactic nuclei, stellar and photo-ionization feedback, and star formation (SF). The software can determine the stellar mass function and stellar–halo mass relation at z=0–4; cosmic evolution of the star formation rate density, stellar mass, atomic and molecular hydrogen; local gas scaling relations; and structural galaxy properties. It performs particularly well for the mass–size relation for discs/bulges, the gas–stellar mass and stellar mass–metallicity relations. Shark is written in C++11 and has been parallelized with OpenMP.