# **GWDALI Software**
Software 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.
## Installation
To install the software run the command below:
```
$ pip install gwdali
```
## Documentation
Available in [https://gwdali.readthedocs.io/en/latest/](https://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.
## Authors
- **Josiel Mendonça Soares de Souza** (developer)
- **Riccardo Sturani** (collaborator)
## License
MIT License
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"description": "# **GWDALI Software**\n\nSoftware 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.\n\n\n## Installation\n\nTo install the software run the command below:\n\n```\n$ pip install gwdali\n```\n\n## Documentation\n\nAvailable in [https://gwdali.readthedocs.io/en/latest/](https://gwdali.readthedocs.io/en/latest/)\n \n## Usage [example]\n import numpy as np\n #-------------------\n import GWDALI as gw\n #-------------------\n from tqdm import trange\n from astropy.cosmology import FlatLambdaCDM\n cosmo = FlatLambdaCDM(70,0.3)\n\n rad = np.pi/180 ; deg = 1./rad\n #--------------------------------------------\n # Detector, position and orientation\n #--------------------------------------------\n FreeParams = ['DL','iota','psi','phi_coal']\n\n # Cosmic Explorer:\n det0 = {\"name\":\"CE\",\"lon\":-119,\"lat\":46,\"rot\":45,\"shape\":90}\n # Einstein Telescope:\n det1 = {\"name\":\"ET\",\"lon\":10,\"lat\":43,\"rot\":0,\"shape\":60}\n det2 = {\"name\":\"ET\",\"lon\":10,\"lat\":43,\"rot\":120,\"shape\":60}\n det3 = {\"name\":\"ET\",\"lon\":10,\"lat\":43,\"rot\":-120,\"shape\":60}\n\n #------------------------------------------------------\n # Setting Injections (Single detection)\n #------------------------------------------------------\n z = 0.1 # Redshift\n\n params = {}\n params['m1'] = 1.3*(1+z) # mass of the first object [solar mass]\n params['m2'] = 1.5*(1+z) # mass of the second object [solar mass]\n params['z'] = z\n params['RA'] = np.random.uniform(-180,180)\n params['Dec'] = (np.pi/2-np.arccos(np.random.uniform(-1,1)))*deg\n params['DL'] = cosmo.luminosity_distance(z).value/1.e3 # Gpc\n params['iota'] = np.random.uniform(0,np.pi) # Inclination angle (rad)\n params['psi'] = np.random.uniform(-np.pi,np.pi) # Polarization angle (rad)\n params['t_coal'] = 0 # Coalescence time\n params['phi_coal'] = 0 # Coalescence phase\n # Spins:\n params['sx1'] = 0\n params['sy1'] = 0\n params['sz1'] = 0\n params['sx2'] = 0\n params['sy2'] = 0\n params['sz2'] = 0\n\n #----------------------------------------------------------------------\n # \"approximant\" options:\n # [Leading_Order, TaylorF2_py, ...] or any lal approximant\n #----------------------------------------------------------------------\n # \"dali_method\" options:\n # [Fisher, Fisher_Sampling, Doublet, Triplet, Standard]\n #----------------------------------------------------------------------\n res = gw.GWDALI( Detection_Dict = params,\n FreeParams = FreeParams,\n detectors = [det0,det1,det2,det3], # Einstein Telescope + Cosmic Explorer\n approximant = 'TaylorF2_py',\n dali_method = 'Doublet',\n sampler_method = 'nestle', # Same as Bilby sampling method\n save_fisher = False,\n save_cov = False,\n plot_corner = False,\n save_samples = False,\n hide_info = True,\n index = 1,\n rcond = 1.e-4,\n npoints=300) # points for \"nested sampling\" or steps/walkers for \"MCMC\"\n\n Samples = res['Samples']\n Fisher = res['Fisher']\n CovFish = res['CovFisher']\n Cov = res['Covariance']\n Rec = res['Recovery']\n Err = res['Error']\n SNR = res['SNR']\n\n## References\n\n[1] L. S. Finn and D. F. Chernoff, \u201cObserving binary inspiral in gravitational radiation: One interferometer,\u201d Phys. Rev. D, vol. 47, pp. 2198\u20132219, 1993.\n\n[2] E. Sellentin, M. Quartin, and L. Amendola, \u201cBreaking the spell of gaussianity: forecasting with higher order fisher matrices,\u201d Monthly Notices of the Royal Astronomical Society, vol. 441, no. 2, pp. 1831\u20131840, 2014.\n\n[3] Z. Wang, C. Liu, J. Zhao, and L. Shao, \u201cExtending the fisher information matrix in gravitational-wave data analysis,\u201d arXiv preprint arXiv:2203.02670, 2022.\n\n## Authors\n\n- **Josiel Mendon\u00e7a Soares de Souza** (developer)\n- **Riccardo Sturani** (collaborator)\n\n## License\n\nMIT License\n",
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