pyccl 0.3.1

Library of validated cosmological functions.

CCL

LSST DESC Core Cosmology Library (CCL) provides routines to compute basic cosmological observables with validated numerical accuracy.

The library is written in C99 and all functionality is directly callable from C and C++ code. We also provide python bindings for higher-level functions.

See also our wiki.

Installation

TLDR

CCL is available as a Python package through PyPi. To install, simply run:

$ pip install pyccl

This should work as long as CMake is installed on your system (if it doesn't follow the detailed instructions below). Once CCL is installed, take it for a spin by following some example notebooks here.

CCL comes in two forms, a C library and a Python module. These components can be installed independently of each other, instructions are provided below.

Dependencies and requirements

CCL requires the following software and libraries:

• GSL version 2.1 or above
• FFTW3 version 3.1 or above
• CLASS version 2.6.3 or above
• Angpow
• FFTlog(here and here)is provided within CCL, with minor modifications.

In addition, the build system for CCL relies on the following software:

• CMake version 3.2 or above
• SWIG

CMake is the only requirement that needs to be manually installed:

• On Ubuntu:

$ sudo apt-get install cmake

• On MacOs X:
  • Install using a DMG package from this download page
  • Install using a package manager (brew, MacPorts, Fink). For instance with brew:

  $ brew install cmake
  

It is preferable to install GSL and FFTW on your system before building CCL but only necessary if you want to properly install the C library, otherwise CMake will automatically download and build the missing requirements in order to compile CCL.

To install all the dependencies at once, and avoid having CMake recompiling them, for instance on Ubuntu:

$ sudo apt-get install cmake swig libgsl-dev libfftw3-dev

Compile and install the CCL C library

To download the latest version of CCL:

$ git clone https://github.com/LSSTDESC/CCL.git
$ cd CCL

or download and extract the latest stable release from here. Then, from the base CCL directory run:

$ mkdir build && cd build
$ cmake ..

This will run the configuration script, try to detect the required dependencies on your machine and generate a Makefile. Once CMake has been configured, to build and install the library simply run for the build directory:

$ make
$ make install

Often admin privileges will be needed to install the library. If you have those just type:

$ sudo make install

Note: This is the default install procedure, but depending on your system you might want to customize the intall process. Here are a few common configuration options:

• C compiler: In case you have several C compilers on your machine, you will probably need to specify which one to use to CMake by setting the environment CC like so, before running CMake:

$ export CC=gcc

• Install directory: By default, CMake will try to install CCL in /usr/local, if you would like to instead install CCL in a user-defined directory (for instance if you don't have admin privileges), you can specify it to CMake by running instead the following command:

$ cmake -DCMAKE_INSTALL_PREFIX=/path/to/install ..

This will instruct CMake to install CCL in the following folders: /path/to/install/include,/path/to/install/share ,/path/to/install/lib.

Depending on where you install CCL your might need to add the installation path to your to your PATH and LD_LIBRARY_PATH environment variables. In the default case, it will look like:

export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/lib
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/bin

To make sure that everything is working properly, you can run all unit tests after installation by running from the root CCL directory:

$ check_ccl

Assuming that the tests pass, you have successfully installed CCL!

If you ever need to uninstall CCL, run the following from the build directory:

$ make uninstall

You may need to prepend a sudo if you installed CCL in a protected folder.

Install the pyccl Python module

CCL also comes with a Python wrapper, called pyccl, which can be built and installed regardless of whether you install the C library. For convenience, we provide a PyPi hosted package which can be installed simply by running:

$ pip install pyccl # append --user for single user install

This only assumes that CMake is available on your system, you don't need to download the source yourself.

You can also build and install pyccl from the CCL source, again without necessarily installing the C library. Download the latest version of CCL:

$ git clone https://github.com/LSSTDESC/CCL.git
$ cd CCL

And from the root CCL folder, simply run:

$ python setup.py install # append --user for single user install

The pyccl module will be installed into a sensible location in your PYTHONPATH, and so should be picked up automatically by your Python interpreter. You can then simply import the module using import pyccl.

You can quickly check whether pyccl has been installed correctly by running python -c "import pyccl" and checking that no errors are returned.

For a more in-depth test to make sure everything is working, run from the root CCL directory:

$ python setup.py test

This will run the embedded unit tests (may take a few minutes).

Whatever the install method, you can always uninstall the pyton wrapper by running:

$ pip uninstall pyccl

For quick introduction to CCL in Python look at notebooks in tests/.

Known installation issues

1. In case you have several C compilers on your system, CMake may not default to the one you want to use. You can specify which C compiler will be used to compile CCL by setting the CC environment variable before calling any cmake or python setup.py commands:

export CC=gcc

Development workflow

Installing CCL on the system is not a good idea when doing development, you can compile and run all the libraries and examples directly from your local copy. The only subtlety when not actually installing the library is that one needs to define the environment variable CCL_PARAM_FILE pointing to include/ccl_params.ini :

export CCL_PARAM_FILE=/path/to/your/ccl/folder/include/ccl_params.ini

Failure to define this environment variable will result in violent segfaults !

Working on the C library

Here are a few common steps when working on the C library:

• Cloning a local copy and CCL and compiling it:

$ git clone https://github.com/LSSTDESC/CCL
$ mkdir -p CCL/build && cd CCL/build
$ cmake ..
$ make

• Updating local copy from master, recompiling what needs recompiling, and running the test suite:

$ git pull      # From root folder
$ make -Cbuild  # The -C option allows you to run make from a different directory
$ build/check_ccl

• Compiling (or recompiling) an example in the CCL/examples folder:

$ cd examples  # From root folder
$ make -C../build ccl_sample_pkemu
$ ./ccl_sample_pkemu

• Reconfiguring from scratch (in case something goes terribly wrong):

$ cd build
$ rm -rf *
$ cmake ..
$ make

Working on the Python library

Here are a few common steps when working on the Python module:

• Building the python module:

$ python setup.py build

After that, you can start your interpreter from the root CCL folder and import pyccl

• Running the tests after a modification of the C library:

$ python setup.py build
$ python setup.py test

Compiling against an external version of CLASS

The default installation procedure for CCL implies automatically downloading and installing a tagged version of CLASS. Optionally, you can also link CCL against a different version of CLASS. This is useful if you want to use a modified version of CLASS, or a different or more up-to-date version of the standard CLASS.

To compile CCL with an external version of CLASS, just run the following CMake command at the first configuration step of the install (from the build directory, make sure it is empty to get a clean configuration):

$ cmake -DEXTERNAL_CLASS_PATH=/path/to/class ..

the rest of the build process should be the same.

Docker image installation

The Dockerfile to generate a Docker image is included in the CCL repository as Dockerfile. This can be used to create an image that Docker can spool up as a virtual machine, allowing you to utilize CCL on any infrastructure with minimal hassle. The details of Docker and the installation process can be found at https://www.docker.com/. Once Docker is installed, it is a simple process to create an image! In a terminal of your choosing (with Docker running), type the command docker build -t ccl . in the CCL directory.

The resulting Docker image has two primary functionalities. The first is a CMD that will open Jupyter notebook tied to a port on your local machine. This can be used with the following run command: docker run -p 8888:8888 ccl. You can then access the notebook in the browser of your choice at localhost:8888. The second is to access the bash itself, which can be done using docker run -it ccl bash.

This Dockerfile currently contains all installed C libraries and the Python wrapper. It currently uses continuumio/anaconda as the base image and supports ipython and Jupyter notebook. There should be minimal slowdown due to the virtualization.

Documentation

CCL has basic doxygen documentation for its C routines. This can be found in the directory doc/html within the CCL repository by opening the index.html file in your browser. The python routines are documented in situ; you can view the documentation for a function by calling help(function name) from within python.

This document contains basic information about used structures and functions. At the end of document is provided code which implements these basic functions (also in examples/ccl_sample_run.c). More information about CCL functions and implementation can be found in doc/0000-ccl_note/0000-ccl_note.pdf.

Cosmological parameters

Start by defining cosmological parameters defined in structure ccl_parameters. This structure (exact definition in include/ccl_core.h) contains densities of matter, parameters of dark energy (w0, wa), Hubble parameters, primordial power spectra, radiation parameters, derived parameters (sigma_8, Omega_1, z_star) and modified growth rate.

Currently, the following families of models are supported:

• Flat ΛCDM
• wCDM and the CPL model (w0 + wa)
• Non-zero curvature (K)
• Arbitrary, user-defined modified growth function
• A single massive neutrino species or multiple equal-mass massive neutrinos (non-compatible with the user-defined modified growth function)

You can initialize this structure through function ccl_parameters_create which returns object of type ccl_parameters.

ccl_parameters ccl_parameters_create(
    double Omega_c, double Omega_b, double Omega_k, double N_nu_rel, double N_nu_mass, double mnu,
    double w0, double wa, double h, double norm_pk, double n_s, int nz_mgrowth, double *zarr_mgrowth,
    double *dfarr_mgrowth, int *status);

where:

• Omega_c: cold dark matter
• Omega_b: baryons
• Omega_k: curvature
• N_nu_rel: Number of relativisitic species
• N_nu_mass: N_nu_mass
• mnu: deneutrino masssc
• w0: Dark energy eqn of state parameter
• wa: Dark energy eqn of state parameter, time variation
• h: Hubble constant in units of 100 km/s/Mpc
• norm_pk: the normalization of the power spectrum, either A_s or sigma_8
• n_s: the power-law index of the primordial power spectrum
• nz_mgrowth: the number of redshifts where the modified growth is provided
• zarr_mgrowth: the array of redshifts where the modified growth is provided
• dfarr_mgrowth: the modified growth function vector provided
• status: Status flag. 0 if there are no errors, nonzero otherwise.

For some specific cosmologies you can also use functions ccl_parameters_create_flat_lcdm, ccl_parameters_create_flat_wcdm, ccl_parameters_create_flat_wacdm, ccl_parameters_create_lcdm, which automatically set some parameters. For more information, see file include/ccl_core.c.

The status flag int status = 0 is passed around in almost every CCL function. Normally zero is returned while nonzero if there were some errors during a function call. For specific cases see documentation for ccl_error.c.

The ccl_cosmology object

For the majority of CCL's functions you need an object of type ccl_cosmology, which can be initialized by function ccl_cosmology_create

ccl_cosmology * ccl_cosmology_create(ccl_parameters params, ccl_configuration config);

Note that the function returns a pointer. Variable params of type ccl_parameters contains cosmological parameters created in previous step. Structure ccl_configuration contains information about methods for computing transfer function, matter power spectrum, the impact of baryons on the matter power spectrum and mass function (for available methods see include/ccl_config.h). In the default configuration default_config, CCL will use the following set-up:

const ccl_configuration default_config = {ccl_boltzmann_class, ccl_halofit, ccl_nobaryons, ccl_tinker};

After you are done working with this cosmology object, you should free its work space by ccl_cosmology_free

void ccl_cosmology_free(ccl_cosmology * cosmo);

Distances, Growth factor and Density parameter functions

With defined cosmology we can now compute distances, growth factor (and rate), sigma_8 or density parameters. For comoving radial distance you can call function ccl_comoving_radial_distance

double ccl_comoving_radial_distance(ccl_cosmology * cosmo, double a, int* status);

which returns distance to scale factor a in units of Mpc. For luminosity distance call function ccl_luminosity_distance

double ccl_luminosity_distance(ccl_cosmology * cosmo, double a, int * status);

which also returns distance in units of Mpc. For growth factor (normalized to 1 at z = 0) at sale factor a call ccl_growth_factor

double ccl_growth_factor(ccl_cosmology * cosmo, double a, int * status);

For evaluating density parameters (e.g. matter, dark energy or radiation) call function ccl_omega_x

double ccl_omega_x(ccl_cosmology * cosmo, double a, ccl_omega_x_label label, int* status);

where ccl_omega_x_label label defines species type: 'matter' (0), 'dark_energy'(1), 'radiation'(2), and 'curvature'(3).

For more routines to compute distances, growth rates and density parameters (e.g. at multiple times at once) see file include/ccl_background.h

Matter power spectra and sigma_8

For given cosmology we can compute linear and non-linear matter power spectra using functions ccl_linear_matter_power and ccl_nonlin_matter_power

double ccl_linear_matter_power(ccl_cosmology * cosmo, double k, double a,int * status);
double ccl_nonlin_matter_power(ccl_cosmology * cosmo, double k, double a,int * status);

It is possible to incorporate the impact of baryonic processes on the total matter power spectrum via the baryons_power_spectrum flag is set to ccl_bcm. Please see the CCL note for details on the implementation. Sigma_8 can be calculated by function ccl_sigma8, or more generally by function ccl_sigmaR, which computes the variance of the density field smoothed by spherical top-hat window function on a comoving distance R (in Mpc).

double ccl_sigmaR(ccl_cosmology *cosmo, double R, int * status);
double ccl_sigma8(ccl_cosmology *cosmo, int * status);

These and other functions for different matter power spectra can be found in file include/ccl_power.h.

Angular power spectra

CCL can compute angular power spectra for three tracer types: galaxy number counts, galaxy weak lensing and CMB lensing. Tracer parameters are defined in structure CCL_ClTracer. In general, you can create this object with function ccl_cl_tracer

CCL_ClTracer *ccl_cl_tracer(ccl_cosmology *cosmo,int tracer_type,
				int has_rsd,int has_magnification,int has_intrinsic_alignment,
				int nz_n,double *z_n,double *n,
				int nz_b,double *z_b,double *b,
				int nz_s,double *z_s,double *s,
				int nz_ba,double *z_ba,double *ba,
				int nz_rf,double *z_rf,double *rf,
				double z_source, int * status);

Exact definition of these parameters are described in file include/ccl_cls.h. Usually you can use simplified versions of this function, namely ccl_cl_tracer_number_counts, ccl_cl_tracer_number_counts_simple, ccl_cl_tracer_lensing, ccl_cl_tracer_lensing_simple or ccl_cl_tracer_cmblens. Two most simplified versions (one for number counts and one for shear) take parameters:

CCL_ClTracer *ccl_cl_tracer_number_counts_simple(ccl_cosmology *cosmo,
						     int nz_n,double *z_n,double *n,
                                                     int nz_b,double *z_b,double *b, int * status);
CCL_ClTracer *ccl_cl_tracer_lensing_simple(ccl_cosmology *cosmo,
					       int nz_n,double *z_n,double *n, int * status);

where nz_n is dimension (number of bins) of arrays z_n and n. z_n and n are arrays for the number count of objects per redshift interval (arbitrary normalization - renormalized inside). nz_b, z_b and b are the same for the clustering bias.

Before computing the angular power spectrum, users must define a workspace structure that contains the relevant parameters for the computation:

CCL_ClWorkspace *ccl_cl_workspace_default(int lmax,int l_limber,int non_limber_method,
					  double l_logstep,int l_linstep,
					  double dchi,double dlk,double zmin,int *status)

where lmax sets the maximum multipole, l_limber the limit multipole from which the Limber approximation is used (l_limber=-1 means that the Liber approximation is never used). The non_limber_method variable can be set to CCL_NONLIMBER_METHOD_NATIVE or CCL_NONLIMBER_METHOD_ANGPOW to choose the method to compute the non-Limber part of the angular power spectrum (either the native CCL code or the Angpow library). Then l_linstep sets the maximum multipole until which the angular power spectrum is computed at each multipole, and l_logstep the logarithmic stepping to use above l_linstep (then the power spectrum is interpolated at each multipole). dchi sets the interval in comoving distance to use for the native non-Limber computation and dlkthe logarithmic stepping for the Fourier k-integration (Angpow is not concerned by these two parameters). A simplified workspace is provided for computations that use only the Limber approximation at each multipole:

CCL_ClWorkspace *ccl_cl_workspace_default_limber(int lmax,double l_logstep,int l_linstep,
						 double dlk,int *status)

With initialized tracers and workspace you can compute limber power spectrum with ccl_angular_cls

double ccl_angular_cls(ccl_cosmology *cosmo,int l,CCL_ClTracer *clt1,CCL_ClTracer *clt2,
						int nl_out,int *l_out,double *cl_out,int * status);

with l_out and cl_out arrays of size nl_out that contains the multipoles and the angular power spectrum.

After you are done working with tracers, you should free its work space by ccl_cl_tracer_free and ccl_cl_workspace_free

void ccl_cl_tracer_free(CCL_ClTracer *clt);
void ccl_cl_workspace_free(CCL_ClWorkspace *w);

Note that for the moment Angpow can not handle the magnification lensing term for the galaxy number count tracers, and has not been tested for the weak lensing tracer. This limitations will be removed in the near future.

Halo mass function

The halo mass function dN/dM can be obtained by function ccl_massfunc

double ccl_massfunc(ccl_cosmology * cosmo, double smooth_mass, double a, double odelta, int * status);

where smooth_mass is mass smoothing scale (in units of M_sun) and odelta is choice of Delta. For more details (or other functions like sigma_M) see include/ccl_massfunc.h and src/mass_func.c.

LSST Specifications

CCL includes LSST specifications for the expected galaxy distributions of the full galaxy clustering sample and the lensing source galaxy sample. Start by defining a flexible photometric redshift model given by function

double (* your_pz_func)(double z_ph, double z_s, void *param, int * status);

which returns the likelihood of measuring a particular photometric redshift z_ph given a spectroscopic redshift z_s, with a pointer to additional arguments param and a status flag. Then you call function ccl_specs_create_photoz_info

user_pz_info* ccl_specs_create_photoz_info(void * user_params,
                                           double(*user_pz_func)(double, double, void*, int*));

which creates a strcture user_pz_info which holds information needed to compute dN/dz

typedef struct {
  double (* your_pz_func)(double, double, void *, int*);
  void *  your_pz_params;
} user_pz_info;

The expected dN/dz for lensing or clustering galaxies with given binning can be obtained by function ccl_specs_dNdz_tomog

void ccl_specs_dNdz_tomog(double z, int dNdz_type, double bin_zmin, double bin_zmax,
                          user_pz_info * user_info,  double *tomoout, int *status);

Result is returned in tomoout. Allowed types of dNdz_type (currently one for clustering and three for lensing - fiducial, optimistic, and conservative - cases are considered) and other information and functions like bias clustering or sigma_z are specified in file include/ccl_lsst_specs.h

After you are done working with photo_z, you should free its work space by ccl_specs_free_photoz_info

void ccl_specs_free_photoz_info(user_pz_info *my_photoz_info);

Example code

This code can also be found in examples/ccl_sample_run.c You can run the following example code. For this you will need to compile with the following command:

gcc -Wall -Wpedantic -g -I/path/to/install/include -std=gnu99 -fPIC examples/ccl_sample_run.c \
-o examples/ccl_sample_run -L/path/to/install/lib -L/usr/local/lib -lgsl -lgslcblas -lm -lccl

where /path/to/install/ is the path to the location where the library has been installed.

#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "ccl.h"
#include "ccl_lsst_specs.h"

#define OC 0.25
#define OB 0.05
#define OK 0.00
#define ON 0.00
#define HH 0.70
#define W0 -1.0
#define WA 0.00
#define NS 0.96
#define NORMPS 0.80
#define ZD 0.5
#define NZ 128
#define Z0_GC 0.50
#define SZ_GC 0.05
#define Z0_SH 0.65
#define SZ_SH 0.05
#define NL 512
#define PS 0.1
#define NREL 3.046
#define NMAS 0
#define MNU 0.0



// The user defines a structure of parameters
// to the user-defined function for the photo-z probability
struct user_func_params
{
  double (* sigma_z) (double);
};

// The user defines a function of the form double function ( z_ph, z_s, void * user_pz_params)
// where user_pz_params is a pointer to the parameters of the user-defined function.
// This returns the probabilty of obtaining a given photo-z given a particular spec_z.
double user_pz_probability(double z_ph, double z_s, void * user_par, int * status)
{
  double sigma_z = ((struct user_func_params *) user_par)->sigma_z(z_s);
  return exp(- (z_ph-z_s)*(z_ph-z_s) / (2.*sigma_z*sigma_z)) / (pow(2.*M_PI,0.5)*sigma_z);
}

int main(int argc,char **argv)
{
  //status flag
  int status =0;

  // Initialize cosmological parameters
  ccl_configuration config=default_config;
  config.transfer_function_method=ccl_boltzmann_class;
  ccl_parameters params = ccl_parameters_create(OC, OB, OK, NREL, NMAS, MNU, W0, WA, HH,
  		 	  			NORMPS, NS,-1,-1,-1,-1,NULL,NULL, &status);
  //printf("in sample run w0=%1.12f, wa=%1.12f\n", W0, WA);

  // Initialize cosmology object given cosmo params
  ccl_cosmology *cosmo=ccl_cosmology_create(params,config);

  // Compute radial distances (see include/ccl_background.h for more routines)
  printf("Comoving distance to z = %.3lf is chi = %.3lf Mpc\n",
	 ZD,ccl_comoving_radial_distance(cosmo,1./(1+ZD), &status));
  printf("Luminosity distance to z = %.3lf is chi = %.3lf Mpc\n",
	 ZD,ccl_luminosity_distance(cosmo,1./(1+ZD), &status));
  printf("Distance modulus to z = %.3lf is mu = %.3lf Mpc\n",
	 ZD,ccl_distance_modulus(cosmo,1./(1+ZD), &status));


  //Consistency check
  printf("Scale factor is a=%.3lf \n",1./(1+ZD));
  printf("Consistency: Scale factor at chi=%.3lf Mpc is a=%.3lf\n",
	 ccl_comoving_radial_distance(cosmo,1./(1+ZD), &status),
	 ccl_scale_factor_of_chi(cosmo,ccl_comoving_radial_distance(cosmo,1./(1+ZD), &status), &status));

  // Compute growth factor and growth rate (see include/ccl_background.h for more routines)
  printf("Growth factor and growth rate at z = %.3lf are D = %.3lf and f = %.3lf\n",
	 ZD, ccl_growth_factor(cosmo,1./(1+ZD), &status),ccl_growth_rate(cosmo,1./(1+ZD), &status));

  // Compute Omega_m, Omega_L and Omega_r at different times
  printf("z\tOmega_m\tOmega_L\tOmega_r\n");
  double Om, OL, Or;
  for (int z=10000;z!=0;z/=3){
    Om = ccl_omega_x(cosmo, 1./(z+1), ccl_omega_m_label, &status);
    OL = ccl_omega_x(cosmo, 1./(z+1), ccl_omega_l_label, &status);
    Or = ccl_omega_x(cosmo, 1./(z+1), ccl_omega_g_label, &status);
    printf("%i\t%.3f\t%.3f\t%.3f\n", z, Om, OL, Or);
  }
  Om = ccl_omega_x(cosmo, 1., ccl_omega_m_label, &status);
  OL = ccl_omega_x(cosmo, 1., ccl_omega_l_label, &status);
  Or = ccl_omega_x(cosmo, 1., ccl_omega_g_label, &status);
  printf("%i\t%.3f\t%.3f\t%.3f\n", 0, Om, OL, Or);

  // Compute sigma_8
  printf("Initializing power spectrum...\n");
  printf("sigma_8 = %.3lf\n\n", ccl_sigma8(cosmo, &status));

  //Create tracers for angular power spectra
  double z_arr_gc[NZ],z_arr_sh[NZ],nz_arr_gc[NZ],nz_arr_sh[NZ],bz_arr[NZ];
  for(int i=0;i<NZ;i++) {
    z_arr_gc[i]=Z0_GC-5*SZ_GC+10*SZ_GC*(i+0.5)/NZ;
    nz_arr_gc[i]=exp(-0.5*pow((z_arr_gc[i]-Z0_GC)/SZ_GC,2));
    bz_arr[i]=1+z_arr_gc[i];
    z_arr_sh[i]=Z0_SH-5*SZ_SH+10*SZ_SH*(i+0.5)/NZ;
    nz_arr_sh[i]=exp(-0.5*pow((z_arr_sh[i]-Z0_SH)/SZ_SH,2));
  }

  //CMB lensing tracer
  CCL_ClTracer *ct_cl=ccl_cl_tracer_cmblens_new(cosmo,1100.,&status);

  //Galaxy clustering tracer
  CCL_ClTracer *ct_gc=ccl_cl_tracer_number_counts_simple_new(cosmo,NZ,
                                z_arr_gc,nz_arr_gc,NZ,z_arr_gc,bz_arr, &status);

  //Cosmic shear tracer
  CCL_ClTracer *ct_wl=ccl_cl_tracer_lensing_simple_new(cosmo,NZ,z_arr_sh,nz_arr_sh, &status);
  printf("ell C_ell(c,c) C_ell(c,g) C_ell(c,s) C_ell(g,g) C_ell(g,s) C_ell(s,s) \n");
  for(int l=2;l<=NL;l*=2) {
    double cl_cc=ccl_angular_cl(cosmo,l,ct_cl,ct_cl, &status); //CMBLensing-CMBLensing
    double cl_cg=ccl_angular_cl(cosmo,l,ct_cl,ct_gc, &status); //CMBLensing-Clustering
    double cl_cs=ccl_angular_cl(cosmo,l,ct_wl,ct_cl, &status); //CMBLensing-Galaxy lensing
    double cl_gg=ccl_angular_cl(cosmo,l,ct_gc,ct_gc, &status); //Galaxy-galaxy
    double cl_gs=ccl_angular_cl(cosmo,l,ct_gc,ct_wl, &status); //Galaxy-lensing
    double cl_ss=ccl_angular_cl(cosmo,l,ct_wl,ct_wl, &status); //Lensing-lensing
    printf("%d %.3lE %.3lE %.3lE %.3lE %.3lE %.3lE\n",l,cl_cc,cl_cg,cl_cs,cl_gg,cl_gs,cl_ss);
  }
  printf("\n");

  //Free up tracers
  ccl_cl_tracer_free(ct_gc);
  ccl_cl_tracer_free(ct_cl);
  ccl_cl_tracer_free(ct_wl);

  //Halo mass function
  printf("M\tdN/dlog10M(z = 0, 0.5, 1))\n");
  for(int logM=9;logM<=15;logM+=1) {
    printf("%.1e\t",pow(10,logM));
    for(double z=0; z<=1; z+=0.5) {
      printf("%e\t", ccl_massfunc(cosmo, pow(10,logM),1.0/(1.0+z), 200., &status));
    }
    printf("\n");
  }
  printf("\n");

  //Halo bias
  printf("Halo bias: z, M, b1(M,z)\n");
  for(int logM=9;logM<=15;logM+=1) {
    for(double z=0; z<=1; z+=0.5) {
      printf("%.1e %.1e %.2e\n",1.0/(1.0+z),pow(10,logM),ccl_halo_bias(cosmo,pow(10,logM),1.0/(1.0+z), 200., &status));
    }
  }
  printf("\n");

  // LSST Specification
  // The user declares and sets an instance of parameters to their photo_z function:
  struct user_func_params my_params_example;
  my_params_example.sigma_z = ccl_specs_sigmaz_sources;

  // Declare a variable of the type of user_pz_info to hold the struct to be created.
  user_pz_info * pz_info_example;

  // Create the struct to hold the user information about photo_z's.
  pz_info_example = ccl_specs_create_photoz_info(&my_params_example, &user_pz_probability);

  // Alternatively, we could have used the built-in Gaussian photo-z pdf,
  // which assumes sigma_z = sigma_z0 * (1 + z) (not used in what follows).
  double sigma_z0 = 0.05;
  user_pz_info *pz_info_gaussian;
  pz_info_gaussian = ccl_specs_create_gaussian_photoz_info(sigma_z0);

  double z_test;
  double dNdz_tomo;
  int z;
  FILE * output;

  //Try splitting dNdz (lensing) into 5 redshift bins
  double tmp1,tmp2,tmp3,tmp4,tmp5;
  printf("Trying splitting dNdz (lensing) into 5 redshift bins. "
         "Output written into file tests/specs_example_tomo_lens.out\n");
  output = fopen("./tests/specs_example_tomo_lens.out", "w");

  if(!output) {
    fprintf(stderr, "Could not write to 'tests' subdirectory"
                    " - please run this program from the main CCL directory\n");
    exit(1);
  }
  status = 0;
  for (z=0; z<100; z=z+1) {
    z_test = 0.035*z;
    ccl_specs_dNdz_tomog(z_test, DNDZ_WL_FID, 0.,6., pz_info_example,&dNdz_tomo,&status);
    ccl_specs_dNdz_tomog(z_test, DNDZ_WL_FID, 0.,0.6, pz_info_example,&tmp1,&status);
    ccl_specs_dNdz_tomog(z_test, DNDZ_WL_FID, 0.6,1.2, pz_info_example,&tmp2,&status);
    ccl_specs_dNdz_tomog(z_test, DNDZ_WL_FID, 1.2,1.8, pz_info_example,&tmp3,&status);
    ccl_specs_dNdz_tomog(z_test, DNDZ_WL_FID, 1.8,2.4, pz_info_example,&tmp4,&status);
    ccl_specs_dNdz_tomog(z_test, DNDZ_WL_FID, 2.4,3.0, pz_info_example,&tmp5,&status);
    fprintf(output, "%f %f %f %f %f %f %f\n", z_test,tmp1,tmp2,tmp3,tmp4,tmp5,dNdz_tomo);
  }

  fclose(output);

  //Try splitting dNdz (clustering) into 5 redshift bins
  printf("Trying splitting dNdz (clustering) into 5 redshift bins. "
         "Output written into file tests/specs_example_tomo_clu.out\n");
  output = fopen("./tests/specs_example_tomo_clu.out", "w");     
  for (z=0; z<100; z=z+1) {
    z_test = 0.035*z;
    ccl_specs_dNdz_tomog(z_test, DNDZ_NC,0.,6., pz_info_example,&dNdz_tomo,&status);
    ccl_specs_dNdz_tomog(z_test, DNDZ_NC,0.,0.6, pz_info_example,&tmp1,&status);
    ccl_specs_dNdz_tomog(z_test, DNDZ_NC,0.6,1.2, pz_info_example,&tmp2,&status);
    ccl_specs_dNdz_tomog(z_test, DNDZ_NC,1.2,1.8, pz_info_example,&tmp3,&status);
    ccl_specs_dNdz_tomog(z_test, DNDZ_NC,1.8,2.4, pz_info_example,&tmp4,&status);
    ccl_specs_dNdz_tomog(z_test, DNDZ_NC,2.4,3.0, pz_info_example,&tmp5,&status);
    fprintf(output, "%f %f %f %f %f %f %f\n", z_test,tmp1,tmp2,tmp3,tmp4,tmp5,dNdz_tomo);
  }
  printf("ccl_sample_run completed, status = %d\n",status);
  fclose(output);

  //Free up photo-z info
  ccl_specs_free_photoz_info(pz_info_example);

  //Always clean up!!
  ccl_cosmology_free(cosmo);

  return 0;
}

Python wrapper

A Python wrapper for CCL is provided through a module called pyccl. The whole CCL interface can be accessed through regular Python functions and classes, with all of the computation happening in the background through the C code. The functions all support numpy arrays as inputs and outputs, with any loops being performed in the C code for speed.

The Python module has essentially the same functions as the C library, just presented in a more standard Python-like way. You can inspect the available functions and their arguments by using the built-in Python help() function, as with any Python module.

Below is a simple example Python script that creates a new Cosmology object, and then uses it to calculate the angular power spectra for a simple lensing cross-correlation. It should take a few seconds on a typical laptop.

import pyccl as ccl
import numpy as np

# Create new Cosmology object with a given set of parameters. This keeps track
# of previously-computed cosmological functions
cosmo = ccl.Cosmology(Omega_c=0.27, Omega_b=0.045, h=0.67, A_s=1e-10, n_s=0.96)

# Define a simple binned galaxy number density curve as a function of redshift
z_n = np.linspace(0., 1., 200)
n = np.ones(z_n.shape)

# Create objects to represent tracers of the weak lensing signal with this
# number density (with has_intrinsic_alignment=False)
lens1 = ccl.ClTracerLensing(cosmo, False, n=(z_n, n))
lens2 = ccl.ClTracerLensing(cosmo, False, n=(z_n, n))

# Calculate the angular cross-spectrum of the two tracers as a function of ell
ell = np.arange(2, 10)
cls = ccl.angular_cl(cosmo, lens1, lens2, ell)
print cls

License, Credits, Feedback etc

The CCL is still under development and should be considered research in progress. You are welcome to re-use the code, which is open source and available under terms consistent with BSD 3-Clause licensing. If you make use of any of the ideas or software in this package in your own research, please cite them as "(LSST DESC, in preparation)" and provide a link to this repository: https://github.com/LSSTDESC/CCL. For free use of the CLASS library, the CLASS developers require that the CLASS paper be cited: CLASS II: Approximation schemes, D. Blas, J. Lesgourgues, T. Tram, arXiv:1104.2933, JCAP 1107 (2011) 034. The CLASS repository can be found in http://class-code.net. If you have comments, questions, or feedback, please write us an issue. Finally, CCL uses code from the FFTLog package. We have obtained permission from the FFTLog author to include modified versions of his source code.