SONG（二阶非高斯性）是一种玻尔兹曼代码，用于.zip

## UPDATE: SONG is looking for a maintainer Find out more at * https://github.com/coccoinomane/song/issues/10 ## DESCRIPTION SONG computes the non-linear evolution of the Universe in order to predict cosmological observables such as the bispectrum of the Cosmic Microwave Background (CMB). More precisely, SONG (Second Order Non-Gaussianity) is a second-order Boltzmann code, as it solves the Einstein and Boltzmann equations up to second order in the cosmological perturbations; the physics, mathematics and numerics of SONG are described extensively in my publicly available [PhD thesis][10], especially in Chapters 5 and 6. The reason for writing SONG was not to provide a more accurate version of the already existing first-order Boltzmann codes, such as [CAMB][1] or [CLASS][2]. Rather, SONG is a tool that, given a cosmological model, provides predictions for "new" observables or probes that do not exist at first order, such as * the intrinsic bispectrum of the CMB ([[3]] and [[4]]), * the angular power spectrum of the spectral distortions [[5]], * the power spectrum of the magnetic fields generated around and after recombination [[11]], * the angular power spectrum of the B-mode polarisation [[6]], * the Fourier bispectrum of the cold dark matter density fluctuations. SONG's structure is based on that of [CLASS][1], a linear Boltzmann code introduced in 2013 [[9]]. In particular, SONG inherits the philosophy of CLASS, that is to provide an easy-to-use interface built on a modular and flexible internal structure. Special care is taken to avoid the use of hard-coded numerical values, or "magic numbers"; the physical and numerical parameters are controlled through two separate input files by the user, who needs to set only those parameters of their interest, the others taking default values. In writing SONG we have followed the principle of encapsulation, so that if you want to modify or add a feature to SONG, you have to edit the code in few localised portions. When in doubt, you can resort to the internal documentation, which comprises more than 10,000 lines of comments. ## MAIN FEATURES OF SONG Here is a summary of the most relevant properties of SONG: * SONG is an open-source project written in C using only freely distributed libraries. * It is fast: it takes about an hour on a modern laptop to compute the intrinsic bispectrum at 10% precision. * It employs an ad-hoc differential evolver designed for stiff systems [[9]]. * It fully includes CMB polarisation at second order. * It implements the tight coupling approximation for faster computation. * It implements a Fisher matrix module to quantify the observability of any intrinsic or primordial bispectrum. * It uses novel algorithms for Bessel convolution, bispectrum integration and 3D interpolation. * It implements the concept of beta-moments, whereby the non-realitivistic and relativistic species are treated in a unified way in terms of the moments of the distribution function. * It inherits from CLASS a modular and flexible structure. * It is OpenMP parallelised. * Its source code is extensively documented with more than 10,000 lines of comments. ## DOCUMENTATION SONG's source code is extensively documented with more than 10,000 lines of comments. The physical and numerical steps are explained in the source (.c) files, while the employed variables are documented in the header (.h) files. The physics, mathematics and numerics of SONG are described extensively in my PhD thesis [[10]], especially in Chapters 5 and 6. For any doubt or enquiry, please email me at <guido.pettinari@gmail.com>. ## GETTING STARTED First, download SONG. You can do so either from the project's page <https://github.com/coccoinomane/song/releases> or from the command line with: git clone --recursive https://github.com/coccoinomane/song.git The `--recursive` flag is important because it allows to download both SONG and CLASS in one command. To compile and make a test run of SONG, enter SONG's directory and execute the following commands from your terminal: make song ./song ini/intrinsic.ini pre/quick_song_run.pre The first command compiles the code using the instructions contained in the file `makefile`. This can be customised to match the configuration of your system. The main variables are the location of the C compiler (gcc by default) and of the OpenMP library (if you want parallelisation); SONG does not rely on any other external library. To compile SONG without parallel support, comment the lines with `-fopenmp` in the Makefile. The second command executes a test run of SONG using the input files `ini/intrinsic.ini` and `pre/quick_song_run.pre`. These are text-only files with a list of "key = value" settings; SONG will read their content and set its internal parameters accordingly. To make a SONG run that will produce an actual physical result, try with ./song ini/intrinsic.ini pre/sn_pol_10percent_lmax2000.pre SONG will output to file and to screen the Fisher matrix and signal-to-noise of the intrinsic bispectrum, with a moderate angular resolution, and a precision of about 10% for both temperature and polarisation; the calculation will take about 40 minutes on an 8-core machine. Feel free to experiment with the parameter files! For example, if you delete `eBisp` from `ini/intrinsic.ini`, SONG will neglect E-polarisation and run much faster. For a guide on what each parameter does, please refer to the (*not yet*) documented file `explanatory.ini` or to the documented `ini/intrinsic.ini`. Use these files as templates for creating your custom input files! ## EXTRACT THE MATTER BISPECTRUM (OR ANY OTHER SOURCE) Running SONG with `ini/matter.ini` and `pre/matter.pre` will compute the dark matter bispectrum delta_cdm(k1,k2,k3,tau) with a sparse sampling consisting of about 25 points in each k direction (from k=10^-5 to k=0.1/Mpc) and about 40 points in the time direction (from tau=280Mpc to today); the computation should take less than a minute on a single processor. The following instructions explains how to extract 1D, 2D and 3D slices from the computed bispectrum. **Please note that what follows applies not only to the bispectrum but to any computed source**, including the CMB & baryon sources; you can specify which sources to compute using the `output` parameter in the ini file. ### Extract 1D Slices To obtain the time evolution of the matter bispectrum for fixed values of (k1,k2,k3) you can run ./print_sources2 matter.ini matter.pre tau <index_k1> <index_k2> <index_k3> where the three k-indices need to be replaced by the indices of (k1,k2,k3) on the k-grid. Similarly, you can obtain the evolution of the matter bispectrum as a function of k2 and k3 (with all other parameters fixed) using the following commands, respectively: ./print_sources2 matter.ini matter.pre k2 <index_k1> <index_k2> <index_tau> ./print_sources2 matter.ini matter.pre k3 <index_k1> <index_k3> <index_tau> Some important points: * To print the k- and tau-grids, you can execute the `print_k_song` and `print_tau_song` giving the ini and pre files as parameters. * If you need specific values of k1, k2, k3, tau or z to be included in the grid, feel free to specify them as comma-separated lists in the `k1_out`, `k2_out`, `k3_out`, `tau_out` and `z_out` parameters in the ini file, respectively. Anything that you add here will be automatically added to the computed grids. Note that `k1_out`, `k2_out` must be given in pairs (see section "2D Slices", below). * The `print_` commands need to be compiled before being executed: `make print_sources2 print_k_song print_tau_song`. ### Extract 2D Slices To extract (k3,tau) slices of the matter bispectrum, and in general of any other computed source, you need to specify some fixed values for (k1,k2) using the `k1_out` and `k2_out` parameters in the ini file. This will generate as many binary files as the number of pairs specified via `k1_out` and `k2_out`