Package: gwdali
GWDALI SoftwareSoftware developed to perform parameter estimations of gravitational waves from compact objects coalescence (CBC) via Gaussian and Beyond-Gaussian approximation of GW likelihood. The Gaussian approximation is related to Fisher Matrix, from which it is direct to compute the covariance matrix by inverting the Fisher Matrix[1]. GWDALI also deals with the not-so-infrequent cases of Fisher Matrix with zero-determinant. The Beyond-Gaussian approach uses the Derivative Approximation for LIkelihoods (DALI) algorithm proposed in[2]and applied to gravitational waves in[3], whose model parameter uncertainties are estimated via Monte Carlo sampling but less costly than using the GW likelihood with no approximation.InstallationTo install the software run the command below:$ pip install gwdaliDocumentationAvailable inhttps://gwdali.readthedocs.io/en/latest/Usage [example]import numpy as np
#-------------------
import GWDALI as gw
#-------------------
from tqdm import trange
from astropy.cosmology import FlatLambdaCDM
cosmo = FlatLambdaCDM(70,0.3)

rad = np.pi/180 ; deg = 1./rad
#--------------------------------------------
# Detector, position and orientation
#--------------------------------------------
FreeParams = ['DL','iota','psi','phi_coal']

# Cosmic Explorer:
det0 = {"name":"CE","lon":-119,"lat":46,"rot":45,"shape":90}
# Einstein Telescope:
det1 = {"name":"ET","lon":10,"lat":43,"rot":0,"shape":60}
det2 = {"name":"ET","lon":10,"lat":43,"rot":120,"shape":60}
det3 = {"name":"ET","lon":10,"lat":43,"rot":-120,"shape":60}

#------------------------------------------------------
# Setting Injections (Single detection)
#------------------------------------------------------
z = 0.1 # Redshift

params = {}
params['m1']  = 1.3*(1+z) # mass of the first object [solar mass]
params['m2']  = 1.5*(1+z) # mass of the second object [solar mass]
params['z']   = z
params['RA']       = np.random.uniform(-180,180)
params['Dec']      = (np.pi/2-np.arccos(np.random.uniform(-1,1)))*deg
params['DL']       = cosmo.luminosity_distance(z).value/1.e3 # Gpc
params['iota']     = np.random.uniform(0,np.pi)          # Inclination angle (rad)
params['psi']      = np.random.uniform(-np.pi,np.pi) # Polarization angle (rad)
params['t_coal']   = 0  # Coalescence time
params['phi_coal'] = 0  # Coalescence phase
# Spins:
params['sx1'] = 0
params['sy1'] = 0
params['sz1'] = 0
params['sx2'] = 0
params['sy2'] = 0
params['sz2'] = 0

#----------------------------------------------------------------------
# "approximant" options:
#               [Leading_Order, TaylorF2_py, ...] or any lal approximant
#----------------------------------------------------------------------
# "dali_method" options:
#               [Fisher, Fisher_Sampling, Doublet, Triplet, Standard]
#----------------------------------------------------------------------
res = gw.GWDALI( Detection_Dict = params,
                 FreeParams     = FreeParams,
                 detectors      = [det0,det1,det2,det3], # Einstein Telescope + Cosmic Explorer
                 approximant    = 'TaylorF2_py',
                 dali_method    = 'Doublet',
                 sampler_method = 'nestle', # Same as Bilby sampling method
                 save_fisher    = False,
                 save_cov       = False,
                 plot_corner    = False,
                 save_samples   = False,
                 hide_info      = True,
                 index          = 1,
                 rcond          = 1.e-4,
                 npoints=300) # points for "nested sampling" or steps/walkers for "MCMC"

Samples = res['Samples']
Fisher  = res['Fisher']
CovFish = res['CovFisher']
Cov     = res['Covariance']
Rec     = res['Recovery']
Err     = res['Error']
SNR     = res['SNR']References[1] L. S. Finn and D. F. Chernoff, “Observing binary inspiral in gravitational radiation: One interferometer,” Phys. Rev. D, vol. 47, pp. 2198–2219, 1993.[2] E. Sellentin, M. Quartin, and L. Amendola, “Breaking the spell of gaussianity: forecasting with higher order fisher matrices,” Monthly Notices of the Royal Astronomical Society, vol. 441, no. 2, pp. 1831–1840, 2014.[3] Z. Wang, C. Liu, J. Zhao, and L. Shao, “Extending the fisher information matrix in gravitational-wave data analysis,” arXiv preprint arXiv:2203.02670, 2022.AuthorsJosiel Mendonça Soares de Souza(developer)Riccardo Sturani(collaborator)LicenseMIT License