def test_broken_powerlaw_prior(self): """Test that red noise signal returns correct values.""" # set up signal parameter pr = gp_priors.broken_powerlaw( log10_A=parameter.Uniform(-18, -12), gamma=parameter.Uniform(1, 7), log10_fb=parameter.Uniform(-9, -7.5), kappa=parameter.Uniform(0.1, 1.0), delta=parameter.Uniform(0.01, 1), ) basis = gp_bases.createfourierdesignmatrix_red(nmodes=30) rn = gp_signals.BasisGP(priorFunction=pr, basisFunction=basis, name="red_noise") rnm = rn(self.psr) # parameters log10_A, gamma, log10_fb, kappa, delta = -14.5, 4.33, -8.5, 1, 0.5 params = { "B1855+09_red_noise_log10_A": log10_A, "B1855+09_red_noise_gamma": gamma, "B1855+09_red_noise_log10_fb": log10_fb, "B1855+09_red_noise_kappa": kappa, "B1855+09_red_noise_delta": delta, } # basis matrix test F, f2 = gp_bases.createfourierdesignmatrix_red(self.psr.toas, nmodes=30) msg = "F matrix incorrect for turnover." assert np.allclose(F, rnm.get_basis(params)), msg # spectrum test phi = gp_priors.broken_powerlaw(f2, log10_A=log10_A, gamma=gamma, log10_fb=log10_fb, kappa=kappa, delta=delta) msg = "Spectrum incorrect for turnover." assert np.all(rnm.get_phi(params) == phi), msg # inverse spectrum test msg = "Spectrum inverse incorrect for turnover." assert np.all(rnm.get_phiinv(params) == 1 / phi), msg # test shape msg = "F matrix shape incorrect" assert rnm.get_basis(params).shape == F.shape, msg
def common_red_noise_block(psd='powerlaw', prior='log-uniform', Tspan=None, components=30, log10_A_val=None, gamma_val=None, delta_val=None, orf=None, orf_ifreq=0, leg_lmax=5, name='gw', coefficients=False, pshift=False, pseed=None): """ Returns common red noise model: 1. Red noise modeled with user defined PSD with 30 sampling frequencies. Available PSDs are ['powerlaw', 'turnover' 'spectrum'] :param psd: PSD to use for common red noise signal. Available options are ['powerlaw', 'turnover' 'spectrum', 'broken_powerlaw'] :param prior: Prior on log10_A. Default if "log-uniform". Use "uniform" for upper limits. :param Tspan: Sets frequency sampling f_i = i / Tspan. Default will use overall time span for individual pulsar. :param log10_A_val: Value of log10_A parameter for fixed amplitude analyses. :param gamma_val: Value of spectral index for power-law and turnover models. By default spectral index is varied of range [0,7] :param delta_val: Value of spectral index for high frequencies in broken power-law and turnover models. By default spectral index is varied in range [0,7]. :param orf: String representing which overlap reduction function to use. By default we do not use any spatial correlations. Permitted values are ['hd', 'dipole', 'monopole']. :param orf_ifreq: Frequency bin at which to start the Hellings & Downs function with numbering beginning at 0. Currently only works with freq_hd orf. :param leg_lmax: Maximum multipole of a Legendre polynomial series representation of the overlap reduction function [default=5] :param pshift: Option to use a random phase shift in design matrix. For testing the null hypothesis. :param pseed: Option to provide a seed for the random phase shift. :param name: Name of common red process """ orfs = { 'crn': None, 'hd': utils.hd_orf(), 'dipole': utils.dipole_orf(), 'monopole': utils.monopole_orf(), 'param_hd': model_orfs.param_hd_orf(a=parameter.Uniform(-1.5, 3.0)('gw_orf_param0'), b=parameter.Uniform(-1.0, 0.5)('gw_orf_param1'), c=parameter.Uniform(-1.0, 1.0)('gw_orf_param2')), 'spline_orf': model_orfs.spline_orf( params=parameter.Uniform(-0.9, 0.9, size=7)('gw_orf_spline')), 'bin_orf': model_orfs.bin_orf( params=parameter.Uniform(-1.0, 1.0, size=7)('gw_orf_bin')), 'zero_diag_hd': model_orfs.zero_diag_hd(), 'zero_diag_bin_orf': model_orfs.zero_diag_bin_orf(params=parameter.Uniform( -1.0, 1.0, size=7)('gw_orf_bin_zero_diag')), 'freq_hd': model_orfs.freq_hd(params=[components, orf_ifreq]), 'legendre_orf': model_orfs.legendre_orf( params=parameter.Uniform(-1.0, 1.0, size=leg_lmax + 1)('gw_orf_legendre')), 'zero_diag_legendre_orf': model_orfs.zero_diag_legendre_orf( params=parameter.Uniform(-1.0, 1.0, size=leg_lmax + 1)('gw_orf_legendre_zero_diag')) } # common red noise parameters if psd in ['powerlaw', 'turnover', 'turnover_knee', 'broken_powerlaw']: amp_name = '{}_log10_A'.format(name) if log10_A_val is not None: log10_Agw = parameter.Constant(log10_A_val)(amp_name) else: if prior == 'uniform': log10_Agw = parameter.LinearExp(-18, -11)(amp_name) elif prior == 'log-uniform' and gamma_val is not None: if np.abs(gamma_val - 4.33) < 0.1: log10_Agw = parameter.Uniform(-18, -14)(amp_name) else: log10_Agw = parameter.Uniform(-18, -11)(amp_name) else: log10_Agw = parameter.Uniform(-18, -11)(amp_name) gam_name = '{}_gamma'.format(name) if gamma_val is not None: gamma_gw = parameter.Constant(gamma_val)(gam_name) else: gamma_gw = parameter.Uniform(0, 7)(gam_name) # common red noise PSD if psd == 'powerlaw': cpl = utils.powerlaw(log10_A=log10_Agw, gamma=gamma_gw) elif psd == 'broken_powerlaw': delta_name = '{}_delta'.format(name) kappa_name = '{}_kappa'.format(name) log10_fb_name = '{}_log10_fb'.format(name) kappa_gw = parameter.Uniform(0.01, 0.5)(kappa_name) log10_fb_gw = parameter.Uniform(-10, -7)(log10_fb_name) if delta_val is not None: delta_gw = parameter.Constant(delta_val)(delta_name) else: delta_gw = parameter.Uniform(0, 7)(delta_name) cpl = gpp.broken_powerlaw(log10_A=log10_Agw, gamma=gamma_gw, delta=delta_gw, log10_fb=log10_fb_gw, kappa=kappa_gw) elif psd == 'turnover': kappa_name = '{}_kappa'.format(name) lf0_name = '{}_log10_fbend'.format(name) kappa_gw = parameter.Uniform(0, 7)(kappa_name) lf0_gw = parameter.Uniform(-9, -7)(lf0_name) cpl = utils.turnover(log10_A=log10_Agw, gamma=gamma_gw, lf0=lf0_gw, kappa=kappa_gw) elif psd == 'turnover_knee': kappa_name = '{}_kappa'.format(name) lfb_name = '{}_log10_fbend'.format(name) delta_name = '{}_delta'.format(name) lfk_name = '{}_log10_fknee'.format(name) kappa_gw = parameter.Uniform(0, 7)(kappa_name) lfb_gw = parameter.Uniform(-9.3, -8)(lfb_name) delta_gw = parameter.Uniform(-2, 0)(delta_name) lfk_gw = parameter.Uniform(-8, -7)(lfk_name) cpl = gpp.turnover_knee(log10_A=log10_Agw, gamma=gamma_gw, lfb=lfb_gw, lfk=lfk_gw, kappa=kappa_gw, delta=delta_gw) if psd == 'spectrum': rho_name = '{}_log10_rho'.format(name) if prior == 'uniform': log10_rho_gw = parameter.LinearExp(-9, -4, size=components)(rho_name) elif prior == 'log-uniform': log10_rho_gw = parameter.Uniform(-9, -4, size=components)(rho_name) cpl = gpp.free_spectrum(log10_rho=log10_rho_gw) if orf is None: crn = gp_signals.FourierBasisGP(cpl, coefficients=coefficients, components=components, Tspan=Tspan, name=name, pshift=pshift, pseed=pseed) elif orf in orfs.keys(): if orf == 'crn': crn = gp_signals.FourierBasisGP(cpl, coefficients=coefficients, components=components, Tspan=Tspan, name=name, pshift=pshift, pseed=pseed) else: crn = gp_signals.FourierBasisCommonGP(cpl, orfs[orf], components=components, Tspan=Tspan, name=name, pshift=pshift, pseed=pseed) elif isinstance(orf, types.FunctionType): crn = gp_signals.FourierBasisCommonGP(cpl, orf, components=components, Tspan=Tspan, name=name, pshift=pshift, pseed=pseed) else: raise ValueError('ORF {} not recognized'.format(orf)) return crn
def common_red_noise_block(psd='powerlaw', prior='log-uniform', Tspan=None, components=30, gamma_val=None, delta_val=None, orf=None, name='gw', coefficients=False, pshift=False, pseed=None): """ Returns common red noise model: 1. Red noise modeled with user defined PSD with 30 sampling frequencies. Available PSDs are ['powerlaw', 'turnover' 'spectrum'] :param psd: PSD to use for common red noise signal. Available options are ['powerlaw', 'turnover' 'spectrum', 'broken_powerlaw'] :param prior: Prior on log10_A. Default if "log-uniform". Use "uniform" for upper limits. :param Tspan: Sets frequency sampling f_i = i / Tspan. Default will use overall time span for individual pulsar. :param gamma_val: Value of spectral index for power-law and turnover models. By default spectral index is varied of range [0,7] :param delta_val: Value of spectral index for high frequencies in broken power-law and turnover models. By default spectral index is varied in range [0,7]. :param orf: String representing which overlap reduction function to use. By default we do not use any spatial correlations. Permitted values are ['hd', 'dipole', 'monopole']. :param pshift: Option to use a random phase shift in design matrix. For testing the null hypothesis. :param pseed: Option to provide a seed for the random phase shift. :param name: Name of common red process """ orfs = {'crn': None, 'hd': utils.hd_orf(), 'dipole': utils.dipole_orf(), 'monopole': utils.monopole_orf()} # common red noise parameters if psd in ['powerlaw', 'turnover', 'turnover_knee','broken_powerlaw']: amp_name = '{}_log10_A'.format(name) if prior == 'uniform': log10_Agw = parameter.LinearExp(-18, -11)(amp_name) elif prior == 'log-uniform' and gamma_val is not None: if np.abs(gamma_val - 4.33) < 0.1: log10_Agw = parameter.Uniform(-18, -14)(amp_name) else: log10_Agw = parameter.Uniform(-18, -11)(amp_name) else: log10_Agw = parameter.Uniform(-18, -11)(amp_name) gam_name = '{}_gamma'.format(name) if gamma_val is not None: gamma_gw = parameter.Constant(gamma_val)(gam_name) else: gamma_gw = parameter.Uniform(0, 7)(gam_name) # common red noise PSD if psd == 'powerlaw': cpl = utils.powerlaw(log10_A=log10_Agw, gamma=gamma_gw) elif psd == 'broken_powerlaw': delta_name = '{}_delta'.format(name) kappa_name = '{}_kappa'.format(name) log10_fb_name = '{}_log10_fb'.format(name) kappa_gw = parameter.Uniform(0.01, 0.5)(kappa_name) log10_fb_gw = parameter.Uniform(-10, -7)(log10_fb_name) if delta_val is not None: delta_gw = parameter.Constant(delta_val)(delta_name) else: delta_gw = parameter.Uniform(0, 7)(delta_name) cpl = gpp.broken_powerlaw(log10_A=log10_Agw, gamma=gamma_gw, delta=delta_gw, log10_fb=log10_fb_gw, kappa=kappa_gw) elif psd == 'turnover': kappa_name = '{}_kappa'.format(name) lf0_name = '{}_log10_fbend'.format(name) kappa_gw = parameter.Uniform(0, 7)(kappa_name) lf0_gw = parameter.Uniform(-9, -7)(lf0_name) cpl = utils.turnover(log10_A=log10_Agw, gamma=gamma_gw, lf0=lf0_gw, kappa=kappa_gw) elif psd == 'turnover_knee': kappa_name = '{}_kappa'.format(name) lfb_name = '{}_log10_fbend'.format(name) delta_name = '{}_delta'.format(name) lfk_name = '{}_log10_fknee'.format(name) kappa_gw = parameter.Uniform(0, 7)(kappa_name) lfb_gw = parameter.Uniform(-9.3, -8)(lfb_name) delta_gw = parameter.Uniform(-2, 0)(delta_name) lfk_gw = parameter.Uniform(-8, -7)(lfk_name) cpl = gpp.turnover_knee(log10_A=log10_Agw, gamma=gamma_gw, lfb=lfb_gw, lfk=lfk_gw, kappa=kappa_gw, delta=delta_gw) if psd == 'spectrum': rho_name = '{}_log10_rho'.format(name) if prior == 'uniform': log10_rho_gw = parameter.LinearExp(-9, -4, size=components)(rho_name) elif prior == 'log-uniform': log10_rho_gw = parameter.Uniform(-9, -4, size=components)(rho_name) cpl = gpp.free_spectrum(log10_rho=log10_rho_gw) if orf is None: crn = gp_signals.FourierBasisGP(cpl, coefficients=coefficients, components=components, Tspan=Tspan, name=name, pshift=pshift, pseed=pseed) elif orf in orfs.keys(): if orf == 'crn': crn = gp_signals.FourierBasisGP(cpl, coefficients=coefficients, components=components, Tspan=Tspan, name=name, pshift=pshift, pseed=pseed) else: crn = gp_signals.FourierBasisCommonGP(cpl, orfs[orf], components=components, Tspan=Tspan, name=name, pshift=pshift, pseed=pseed) elif isinstance(orf, types.FunctionType): crn = gp_signals.FourierBasisCommonGP(cpl, orf, components=components, Tspan=Tspan, name=name, pshift=pshift, pseed=pseed) else: raise ValueError('ORF {} not recognized'.format(orf)) return crn