--- CBiRd ---
Code for Biased tracers in Redshift space
version 0.6 (earlyCBiRd - 21/11/2019)

Contact: Pierre Zhang ([email protected])


Introduction
------------
CBiRd provides correlators in the Effective Field Theory of Large-Scale 
Structure (EFTofLSS)in a pipeline `ready-to-use' to perform cosmological 
analysis of galaxy-redshift surveys data.
Incidentally, CBiRd can provide an 'earlybird' pass to explore the 
cosmos with LSS surveys.

CBiRd computes the following correlators of biased tracers in redshift
space:
- the multipoles l = 0, 2 of the one-loop power 
spectrum described in arXiv:1610.09321 using an FFTLog decomposition of 
the linear power spectrum and analytic evaluation of the loop 
integrals following arXiv:1708.08130. The multipoles are IR-resummed 
using controlled approximations identified in arXiv:1512.06831.

CBiRd consists in:
- C++BiRd: a C++ code for core calculation
- TBiRd: a Python implementation of a Taylor expansion of the power 
spectrum around a reference cosmology for efficient evaluation, 
following arXiv:1606.03633
- Python libraries to correct for observational systematics: 
Alcock-Paczynski effect; window functions; fiber-collision 
corrections described in arXiv:1609.01714.
- MCBiRd: MCMC samplers for a power spectrum and bispectrum analysis of 
galaxy-redshift surveys data based on emcee: arXiv:1202.3665

More details can be found in arXiv:1909.05271 and arXiv:1909.07951


C++ Requirements
----------------
CBiRd is written in C++ with standard ISO C++11. 

Three libraries are required for compilation:
- the GSL library <https://www.gnu.org/software/gsl/>
- the FFTW library <http://www.fftw.org/>
- the Eigen library <http://eigen.tuxfamily.org/> 
The code is provided with the Eigen headers in the source: no 
installation should be required for the Eigen library.

The loop calculation involves a discrete Fourier transformation routine 
from the FFTW library and the use of the Eigen library for efficient 
matrix multiplication.

C++BiRd compiling and running
-----------------------------
Adjust or include paths to the GSL, FFTW and CUBA libraries in 
Makefile, and run 'make'.

To run CBiRd type:
./cbird path/to/inifile

An example inifile can be found in cnest/cbird.ini


C++BiRd Output
--------------
CBiRd generates the power spectrum multipoles stacked horizontally in 
one file:
'PowerSpectra.dat'

First line in the output files (with an '#' at the beginning) is the 
legend for the columns:
# k[h/Mpc]    bi    ... 
It means that the first column is the k's for which the power spectra 
in the other column are evaluated and 'bi' are the EFT coefficients 
multiplying the power spectra Pi(k) in the corresponding column. 
The total power spectrum is then given by:
P(k, z) = bi * Pi(k, z) (sum over i) where z is the redshift.
The next three columns after the first column is the linear part.
The following columns correspond to the 1-loop.


C++BiRd Performances
--------------------
Convergence:
C++BiRd has been tested against Mathematica codes (some can be found in 
the EFTofLSS repository <http://web.stanford.edu/~senatore/>) and 
against an earlier version involving numerical evaluation of the loop 
integrals. The monopole is computed up to permil precision and the 
quadrupole up to half percent.


Python dependencies
-------------------
The following libraries are used: numpy, scipy, emcee
The Taylor expansion uses findiff: <https://github.com/maroba/findiff> 
to compute derivatives by finite differences.
The MCMC sampler is based on emcee: arXiv:1202.3665


TBiRd running
-------------
TBiRd calls CLASS to compute the linear power spectrum and C++BiRd to 
compute the redshift space 1-loop power spectrum through the Python 
wrappers plinear.py and pnonlinear.py. Needless to say, make sure that 
CLASS and C++BiRd are compiled somewhere.

The reference cosmology for the Taylor expansion as well as the paths 
for CLASS and C++BiRd are specified in an inifile. An example can be 
found in tbird.ini.

In Grid.py, adjust the path to the inifile. One can also choose in 
which parameters to expand, the order of the expansion as well as the 
steps for the finite differences for the evaluation of the derivatives. 
Default setting is the one used and described in arXiv:1909.XXXXX.

To run TBiRd, first precompute the derivatives. Make a small grid with 
make_taylorgrid.py that computes all relevant cosmologies around the 
reference one for the finite differences. Some options for 
parellisation are to choose at the top of the file. Then check and 
glue the grid with checkglue_taylorgrid.py.

To apply the Alcock-Paczynski effect, window functions and 
fiber-collision corrections, apply modify_grid_fiberwindow.py to the 
grid. Glue it with glue_taylorprocessgrid.py.

After that, run computederivs.py to calculate the derivatives. 
TBiRd is now ready to use.

To evaluate the power spectrum with TBiRd, first import the library 
Grid.py where the reference cosmology, cosmological parameters to vary, 
etc. are specified. Then, import the library tbird.py, load the 
precomputed derivatives with tbird.load_pder(derivs-filename), and call 
tbird.get_PSTaylor(dtheta, derivatives) where dtheta is the difference 
between the cosmology to evaluate to the reference one. Typically, one 
needs two call twice those functions to load both linear and the 1-loop 
power spectra. Give values for the EFT parameters and compute the total 
power spectrum from TBiRd! (with e.g. get_PSbias(plin, ploop, dfit) in 
tbird.py, providing a dictionary dfit for the EFT parameters. 
Check an alternative implementation in the likelihood function 
lnlike(...) calling computePS(...) in MCMC_taylor.py ) 

TBiRd numerical convergence for a low-order Taylor expansion is 
described in arXiv:1909.07951.


MCBiRd running
--------------
[Documentation under construction]

MCBiRd consists in a bunch of MCMC sampler scripts. MCBiRd features 
likelihoods for the CBiRd correlators. In particular, the 
partially-marginalized likelihood described in arXiv:1909.05271 
where the EFT parameters appearing only linearly in the correlators 
are marginalized over at the level of the likelihood.

MCBiRd is based on emcee: arXiv:1202.3665


References
----------
If using CBiRd in a publication, we would be very grateful if the 
following papers were to be cited:

'The Cosmological Analysis of the SDSS/BOSS data from the Effective 
Field Theory of Large-Scale Structure',
G. d'Amico, J. Gleyzes, N. Kokron, D. Markovic, L. Senatore, P. Zhang, 
F. Beutler, H. Gil-Marin, arXiv:1909.05271

'Efficient Cosmological Analysis of the SDSS/BOSS data from the 
Effective Field Theory of Large-Scale Structure',
T. Colas, G. d'Amico, L. Senatore, P. Zhang, F. Beutler, 
arXiv:1909.07951


Contributors
------------
Developped by: Guido d'Amico (TBiRd), Jerome Gleyzes (MCBiRd) and 
Pierre Zhang (C++BiRd)
Supervised by: Leonardo Senatore (TBiRd, C++BiRd)

Parts of the code has been written with the help of:
F. Beutler, T. Colas, H. Gil-Marin, N. Kokron, M. Lewandowski, 
D. Markovic and A. Perko.