NumCosmo is a free software C library whose main purposes are to test cosmological models using observational data and to provide a set of tools to perform cosmological calculations. The software implements three different probes: cosmic microwave background (CMB), supernovae type Ia (SNeIa) and large scale structure (LSS) information, such as baryonic acoustic oscillations (BAO) and galaxy cluster abundance. The code supports a joint analysis of these data and the parameter space can include cosmological and phenomenological parameters. NumCosmo matter power spectrum and CMB codes were written independent of other implementations such as CMBFAST (ascl:9909.004), CAMB (ascl:1102.026), etc.

The library structure simplifies the inclusion of non-standard cosmological models. Besides the functions related to cosmological quantities, this library also implements mathematical and statistical tools. The former were developed to enable the inclusion of other probes and/or theoretical models and to optimize the codes. The statistical framework comprises algorithms which define likelihood functions, minimization, Monte Carlo, Fisher Matrix and profile likelihood methods.

Approximate Bayesian Computation (ABC) enables parameter inference for complex physical systems in cases where the true likelihood function is unknown, unavailable, or computationally too expensive. It relies on the forward simulation of mock data and comparison between observed and synthetic catalogs. cosmoabc is a Python Approximate Bayesian Computation (ABC) sampler featuring a Population Monte Carlo variation of the original ABC algorithm, which uses an adaptive importance sampling scheme. The code can be coupled to an external simulator to allow incorporation of arbitrary distance and prior functions. When coupled with the numcosmo library, it has been used to estimate posterior probability distributions over cosmological parameters based on measurements of galaxy clusters number counts without computing the likelihood function.