NumCosmo

Cosmological constraints with SNeIa

Cosmological constraints with SNeIa

Description

Example written in Python to obtain constraints (best-fit and covariance matrix) on the cold dark matter density $\Omega_c$ and the dark energy equation of state $w$ parameters, where $w =$ constant, using type Ia supernova (SNeIa) data. In this case, the covariance matrix is obtained via observed Fisher Matrix approach.

Running

To try this example you must have PyGObject installed, and numcosmo built with –enable-introspection option. To run the examples without installing follow the instructions here.

example_fit_snia.py:

#!/usr/bin/python2

try:
  import gi
  gi.require_version('NumCosmo', '1.0')
  gi.require_version('NumCosmoMath', '1.0')
except:
  pass

from math import *
import matplotlib.pyplot as plt
from gi.repository import GObject
from gi.repository import NumCosmo as Nc
from gi.repository import NumCosmoMath as Ncm

#
#  Initializing the library objects, this must be called before 
#  any other library function.
#
Ncm.cfg_init ()

#
#  New homogeneous and isotropic cosmological model NcHICosmoDEXcdm 
#
cosmo = Nc.HICosmo.new_from_name (Nc.HICosmo, "NcHICosmoDEXcdm")

#
#  Setting values for the cosmological model, those not set stay in the
#  default values. Remeber to use the _orig_ version to set the original
#  parameters in case when a reparametrization is used.
#

#
# OO-like
#
cosmo.props.H0      = 70.0
cosmo.props.Omegab  = 0.05
cosmo.props.Omegac  = 0.25
cosmo.props.Omegax  = 0.70
cosmo.props.Tgamma0 = 2.72
cosmo.props.w       = -1.0

#
#  Creating a new Modelset and set cosmo as the HICosmo model to be used.
#
mset = Ncm.MSet ()
mset.set (cosmo)

#
#  Setting parameters Omega_c and w to be fitted.
#
cosmo.props.Omegac_fit = True
cosmo.props.w_fit = True

#
#  Creating a new Distance object optimized to redshift 2.
#
dist = Nc.Distance (zf = 2.0)

#
#  Creating a new Data object from distance modulus catalogs.
#
snia = Nc.DataDistMu.new_from_id (dist, Nc.DataSNIAId.SIMPLE_UNION2_1)

#
#  Creating a new Dataset and add snia to it.
#
dset = Ncm.Dataset ()
dset.append_data (snia)

#
#  Creating a Likelihood from the Dataset.
#
lh = Ncm.Likelihood (dataset = dset)

#
#  Creating a Fit object of type NLOPT using the fitting algorithm ln-neldermead to
#  fit the Modelset mset using the Likelihood lh and using a numerical differentiation
#  algorithm (NUMDIFF_FORWARD) to obtain the gradient (if needed).
#
fit = Ncm.Fit.new (Ncm.FitType.NLOPT, "ln-neldermead", lh, mset, Ncm.FitGradType.NUMDIFF_FORWARD)

#
#  Running the fitter printing messages.
#
fit.run (Ncm.FitRunMsgs.SIMPLE)

#
#  Printing fitting informations.
#
fit.log_info ()

#
#  Calculating the parameters covariance using numerical differentiation.
#
fit.numdiff_m2lnL_covar ()

#
#  Printing the covariance matrix.
# 
fit.log_covar ()

Output:

#----------------------------------------------------------------------------------
# Model fitting. Interating using:
#  - solver:            NLOpt:ln-neldermead
#  - differentiation:   Numerical differentiantion (forward)
#.............
#  Minimum found with precision: |df|/f =  1.00000e-08 and |dx| =  1.00000e-05
#  Elapsed time: 00 days, 00:00:00.0102450
#  iteration            [000047]
#  function evaluations [000048]
#  gradient evaluations [000000]
#  degrees of freedom   [000577]
#  m2lnL     =      562.21916535683 (     562.21917 )
#  Fit parameters:
#     0.230588641762734   -1.02987350210547    
#----------------------------------------------------------------------------------
# Data used:
#   - Union2.1 sample
#----------------------------------------------------------------------------------
# Model[00000]:
#   - NcHICosmo : XCDM - Constant EOS
#----------------------------------------------------------------------------------
# Model parameters
#   -      H0[00]:  70                  [FIXED]
#   -  Omegac[01]:  0.230588641762734   [FREE]
#   -  Omegax[02]:  0.7                 [FIXED]
#   - Tgamma0[03]:  2.72                [FIXED]
#   -      Yp[04]:  0.24                [FIXED]
#   -    ENnu[05]:  3.046               [FIXED]
#   -  Omegab[06]:  0.05                [FIXED]
#   -       w[07]: -1.02987350210547    [FREE]
#----------------------------------------------------------------------------------
# NcmMSet parameters covariance matrix
#                                                  -------------------------------
# Omegac[00000:01] =  0.2306      +/-  0.07183     |  1           | -0.9052      |
#      w[00000:07] = -1.03        +/-  0.1301      | -0.9052      |  1           |
#                                                  -------------------------------

Example Directory