def dm_noise(self, option="powerlaw"):
"""
A term to account for stochastic variations in DM. It is based on spin
noise model, with Fourier amplitudes depending on radio frequency nu
as ~ 1/nu^2.
"""
log10_A = parameter.Uniform(self.params.dmn_lgA[0],
self.params.dmn_lgA[1])
gamma = parameter.Uniform(self.params.dmn_gamma[0],
self.params.dmn_gamma[1])
if option == "powerlaw":
pl = utils.powerlaw(log10_A=log10_A, gamma=gamma, \
components=self.params.red_general_nfouriercomp)
elif option == "turnover":
fc = parameter.Uniform(self.params.sn_fc[0], self.params.sn_fc[1])
pl = powerlaw_bpl(log10_A=log10_A,
gamma=gamma,
fc=fc,
components=self.params.red_general_nfouriercomp)
nfreqs = self.determine_nfreqs(sel_func_name=None)
dm_basis = utils.createfourierdesignmatrix_dm(nmodes=nfreqs,
Tspan=self.params.Tspan,
fref=self.params.fref)
dmn = gp_signals.BasisGP(pl, dm_basis, name='dm_gp')
return dmn
def setUpClass(cls):
"""Setup the Pulsar object."""
# initialize Pulsar class
cls.psr = Pulsar(datadir + "/B1855+09_NANOGrav_9yv1.gls.par",
datadir + "/B1855+09_NANOGrav_9yv1.tim")
cls.F, _ = utils.createfourierdesignmatrix_red(cls.psr.toas, nmodes=30)
cls.Fdm, _ = utils.createfourierdesignmatrix_dm(cls.psr.toas,
freqs=cls.psr.freqs,
nmodes=30)
cls.Feph, cls.feph = utils.createfourierdesignmatrix_ephem(
cls.psr.toas, cls.psr.pos, nmodes=30)
cls.Mm = utils.create_stabletimingdesignmatrix(cls.psr.Mmat)
def setUpClass(cls):
"""Setup the Pulsar object."""
# initialize Pulsar class
cls.psr = Pulsar(datadir + '/B1855+09_NANOGrav_9yv1.gls.par',
datadir + '/B1855+09_NANOGrav_9yv1.tim')
cls.F, _ = utils.createfourierdesignmatrix_red(
cls.psr.toas, nmodes=30)
cls.Fdm, _ = utils.createfourierdesignmatrix_dm(
cls.psr.toas,freqs=cls.psr.freqs, nmodes=30)
tmp = utils.createfourierdesignmatrix_eph(t=cls.psr.toas,
phi=cls.psr.phi,
theta=cls.psr.theta,
nmodes=30)
cls.Fx, cls.Fy, cls.Fz = tmp
cls.Mm = utils.create_stabletimingdesignmatrix(cls.psr.Mmat)
psr = Pulsar(p, t)
psrs.append(psr)
save1 = np.load('noisepars.npy')
save2 = np.load('noisepardict.npy')
save3 = np.load('dpdmpars-maxposprob.npy')
save4 = np.load('dpdmpardict.npy')
Dict = {save2[i]: save1[i] for i in range(len(save2))}
Dict.update({save4[i]: save3[i] for i in range(len(save4))})
# The Big Model
# dm noise
log10_A_dm = parameter.Constant()
gamma_dm = parameter.Constant()
pl_dm = utils.powerlaw(log10_A=log10_A_dm, gamma=gamma_dm)
dm_basis = utils.createfourierdesignmatrix_dm(nmodes=50, Tspan=None)
dmn = gp_signals.BasisGP(pl_dm, dm_basis, name='dm_gp', coefficients=False)
# spin noise
log10_A = parameter.Constant()
gamma = parameter.Constant()
pl = utils.powerlaw(log10_A=log10_A, gamma=gamma)
selection = selections.Selection(selections.no_selection)
spn = gp_signals.FourierBasisGP(pl,
components=50,
Tspan=None,
coefficients=False,
selection=selection,
modes=None)
dp = DPDM.dpdm_block(type_='Bayes')
tm = gp_signals.TimingModel()
def dm_noise_block(gp_kernel='diag',
psd='powerlaw',
nondiag_kernel='periodic',
prior='log-uniform',
Tspan=None,
components=30,
gamma_val=None):
"""
Returns DM noise model:
1. DM noise modeled as a power-law with 30 sampling frequencies
:param psd:
PSD function [e.g. powerlaw (default), turnover, free spectrum]
: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 indivicual pulsar.
:param components:
Number of frequencies in sampling of DM-variations.
:param gamma_val:
If given, this is the fixed slope of the power-law for
powerlaw or turnover DM-variations
"""
# dm noise parameters that are common
if gp_kernel == 'diag':
if psd in ['powerlaw', 'turnover']:
# parameters shared by PSD functions
if prior == 'uniform':
log10_A_dm = parameter.LinearExp(-20, -11)
elif prior == 'log-uniform' and gamma_val is not None:
if np.abs(gamma_val - 4.33) < 0.1:
log10_A_dm = parameter.Uniform(-20, -11)
else:
log10_A_dm = parameter.Uniform(-20, -11)
else:
log10_A_dm = parameter.Uniform(-20, -11)
if gamma_val is not None:
gamma_dm = parameter.Constant(gamma_val)
else:
gamma_dm = parameter.Uniform(0, 7)
# different PSD function parameters
if psd == 'powerlaw':
dm_prior = utils.powerlaw(log10_A=log10_A_dm, gamma=gamma_dm)
elif psd == 'turnover':
kappa_dm = parameter.Uniform(0, 7)
lf0_dm = parameter.Uniform(-9, -7)
dm_prior = utils.turnover(log10_A=log10_A_dm,
gamma=gamma_dm,
lf0=lf0_dm,
kappa=kappa_dm)
if psd == 'spectrum':
if prior == 'uniform':
log10_rho_dm = parameter.LinearExp(-10, -4, size=components)
elif prior == 'log-uniform':
log10_rho_dm = parameter.Uniform(-10, -4, size=components)
dm_prior = free_spectrum(log10_rho=log10_rho_dm)
dm_basis = utils.createfourierdesignmatrix_dm(nmodes=components,
Tspan=Tspan)
elif gp_kernel == 'nondiag':
if nondiag_kernel == 'periodic':
# Periodic GP kernel for DM
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
period = parameter.Uniform(0.2, 5.0)
gam_p = parameter.Uniform(0.1, 30.0)
dm_basis = linear_interp_basis_dm(dt=15 * const.day)
dm_prior = periodic_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell,
gam_p=gam_p,
p=period)
elif nondiag_kernel == 'periodic_rfband':
# Periodic GP kernel for DM with RQ radio-frequency dependence
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
log10_ell2 = parameter.Uniform(2, 7)
alpha_wgt = parameter.Uniform(0.2, 6)
period = parameter.Uniform(0.2, 5.0)
gam_p = parameter.Uniform(0.1, 30.0)
dm_basis = get_tf_quantization_matrix(df=200,
dt=15 * const.day,
dm=True)
dm_prior = tf_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell,
gam_p=gam_p,
p=period,
alpha_wgt=alpha_wgt,
log10_ell2=log10_ell2)
elif nondiag_kernel == 'dmx_like':
# DMX-like signal
log10_sigma = parameter.Uniform(-10, -4)
dm_basis = linear_interp_basis_dm(dt=30 * const.day)
dm_prior = dmx_ridge_prior(log10_sigma=log10_sigma)
dmgp = gp_signals.BasisGP(dm_prior, dm_basis, name='dm_gp')
return dmgp
def dm_noise_block(gp_kernel='diag',
psd='powerlaw',
nondiag_kernel='periodic',
prior='log-uniform',
dt=15,
df=200,
Tspan=None,
components=30,
gamma_val=None,
coefficients=False):
"""
Returns DM noise model:
1. DM noise modeled as a power-law with 30 sampling frequencies
:param psd:
PSD function [e.g. powerlaw (default), spectrum, tprocess]
:param prior:
Prior on log10_A. Default if "log-uniform". Use "uniform" for
upper limits.
:param dt:
time-scale for linear interpolation basis (days)
:param df:
frequency-scale for linear interpolation basis (MHz)
:param Tspan:
Sets frequency sampling f_i = i / Tspan. Default will
use overall time span for indivicual pulsar.
:param components:
Number of frequencies in sampling of DM-variations.
:param gamma_val:
If given, this is the fixed slope of the power-law for
powerlaw, turnover, or tprocess DM-variations
"""
# dm noise parameters that are common
if gp_kernel == 'diag':
if psd in ['powerlaw', 'turnover', 'tprocess', 'tprocess_adapt']:
# parameters shared by PSD functions
if prior == 'uniform':
log10_A_dm = parameter.LinearExp(-20, -11)
elif prior == 'log-uniform' and gamma_val is not None:
if np.abs(gamma_val - 4.33) < 0.1:
log10_A_dm = parameter.Uniform(-20, -11)
else:
log10_A_dm = parameter.Uniform(-20, -11)
else:
log10_A_dm = parameter.Uniform(-20, -11)
if gamma_val is not None:
gamma_dm = parameter.Constant(gamma_val)
else:
gamma_dm = parameter.Uniform(0, 7)
# different PSD function parameters
if psd == 'powerlaw':
dm_prior = utils.powerlaw(log10_A=log10_A_dm, gamma=gamma_dm)
elif psd == 'turnover':
kappa_dm = parameter.Uniform(0, 7)
lf0_dm = parameter.Uniform(-9, -7)
dm_prior = utils.turnover(log10_A=log10_A_dm,
gamma=gamma_dm,
lf0=lf0_dm,
kappa=kappa_dm)
elif psd == 'tprocess':
df = 2
alphas_dm = gpp.InvGamma(df / 2, df / 2, size=components)
dm_prior = gpp.t_process(log10_A=log10_A_dm,
gamma=gamma_dm,
alphas=alphas_dm)
elif psd == 'tprocess_adapt':
df = 2
alpha_adapt_dm = gpp.InvGamma(df / 2, df / 2, size=1)
nfreq_dm = parameter.Uniform(-0.5, 10 - 0.5)
dm_prior = gpp.t_process_adapt(log10_A=log10_A_dm,
gamma=gamma_dm,
alphas_adapt=alpha_adapt_dm,
nfreq=nfreq_dm)
if psd == 'spectrum':
if prior == 'uniform':
log10_rho_dm = parameter.LinearExp(-10, -4, size=components)
elif prior == 'log-uniform':
log10_rho_dm = parameter.Uniform(-10, -4, size=components)
dm_prior = gpp.free_spectrum(log10_rho=log10_rho_dm)
dm_basis = utils.createfourierdesignmatrix_dm(nmodes=components,
Tspan=Tspan)
elif gp_kernel == 'nondiag':
if nondiag_kernel == 'periodic':
# Periodic GP kernel for DM
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
log10_p = parameter.Uniform(-4, 1)
log10_gam_p = parameter.Uniform(-3, 2)
dm_basis = gpk.linear_interp_basis_dm(dt=dt * const.day)
dm_prior = gpk.periodic_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell,
log10_gam_p=log10_gam_p,
log10_p=log10_p)
elif nondiag_kernel == 'periodic_rfband':
# Periodic GP kernel for DM with RQ radio-frequency dependence
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
log10_ell2 = parameter.Uniform(2, 7)
log10_alpha_wgt = parameter.Uniform(-4, 1)
log10_p = parameter.Uniform(-4, 1)
log10_gam_p = parameter.Uniform(-3, 2)
dm_basis = gpk.get_tf_quantization_matrix(df=df,
dt=dt * const.day,
dm=True)
dm_prior = gpk.tf_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell,
log10_gam_p=log10_gam_p,
log10_p=log10_p,
log10_alpha_wgt=log10_alpha_wgt,
log10_ell2=log10_ell2)
elif nondiag_kernel == 'sq_exp':
# squared-exponential GP kernel for DM
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
dm_basis = gpk.linear_interp_basis_dm(dt=dt * const.day)
dm_prior = gpk.se_dm_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell)
elif nondiag_kernel == 'sq_exp_rfband':
# Sq-Exp GP kernel for DM with RQ radio-frequency dependence
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
log10_ell2 = parameter.Uniform(2, 7)
log10_alpha_wgt = parameter.Uniform(-4, 1)
dm_basis = gpk.get_tf_quantization_matrix(df=df,
dt=dt * const.day,
dm=True)
dm_prior = gpk.sf_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell,
log10_alpha_wgt=log10_alpha_wgt,
log10_ell2=log10_ell2)
elif nondiag_kernel == 'dmx_like':
# DMX-like signal
log10_sigma = parameter.Uniform(-10, -4)
dm_basis = gpk.linear_interp_basis_dm(dt=dt * const.day)
dm_prior = gpk.dmx_ridge_prior(log10_sigma=log10_sigma)
dmgp = gp_signals.BasisGP(dm_prior,
dm_basis,
name='dm_gp',
coefficients=coefficients)
return dmgp
pl = utils.powerlaw(log10_A=log10_A, gamma=gamma)
basis = utils.createfourierdesignmatrix_red(Tspan=Tspan,
nmodes=args.nfreqs,
logf=args.logf)
rn = gp_signals.BasisGP(priorFunction=pl,
name='red_noise',
basisFunction=basis)
# timing model
tm = gp_signals.TimingModel(use_svd=False)
model = tm + ef + eq + ec + rn
if args.dm_gp_psrs[0] == args.psr:
dm_basis = utils.createfourierdesignmatrix_dm(Tspan=Tspan,
nmodes=args.nfreqs,
logf=args.logf)
dm_gp = gp_signals.BasisGP(priorFunction=pl,
basisFunction=dm_basis,
name='dm_gp')
model += dm_gp
pta = signal_base.PTA(model(psr))
x0 = np.hstack(p.sample() for p in pta.params)
ndim = len(x0)
pta.get_lnlikelihood(x0)
groups = model_utils.get_parameter_groups(pta)
groups.extend([[pta.param_names.index(p) for p in pta.param_names if fl in p]
def solar_wind_block(n_earth=None,
ACE_prior=False,
include_dmgp=False,
sw_prior=None,
sw_basis=None,
Tspan=None):
"""
Returns Solar Wind DM noise model. Best model from Hazboun, et al (in prep)
Contains a single mean electron density with an auxiliary perturbation
modeled using a gaussian process. The GP has common prior parameters
between all pulsars, but the realizations are different for all pulsars.
Solar Wind DM noise modeled as a power-law with 30 sampling frequencies
:param n_earth:
Solar electron density at 1 AU.
:param ACE_prior:
Whether to use the ACE SWEPAM data as an astrophysical prior.
:param include_dmgp:
Boolean flag to add in a simple power-law DM GP automatically.
:param sw_prior:
Prior function for solar wind Gaussian process. Default is a power law.
:param sw_basis:
Basis to be used for solar wind Gaussian process. Default is to use the
built in function to creat a GP with 15 frequencies (1/Tspan,15/Tspan).
:param Tspan:
Sets frequency sampling f_i = i / Tspan. Default will
use overall time span for indivicual pulsar.
"""
# dm noise parameters that are common
if sw_prior is None:
log10_A_sw = parameter.Uniform(-10, 1)('log10_A_sw')
gamma_sw = parameter.Uniform(-2, 1)('gamma_sw')
sw_prior = utils.powerlaw(log10_A=log10_A_sw, gamma=gamma_sw)
if n_earth is None and ACE_prior:
n_earth = parameter.Uniform(0, 30)('n_earth')
elif n_earth is None and not ACE_prior:
n_earth = ACE_SWEPAM_Parameter()('n_earth')
else:
pass
if sw_basis is None:
sw_basis = createfourierdesignmatrix_solar_dm(nmodes=15, Tspan=Tspan)
else:
pass
gp_sw = gp_signals.BasisGP(sw_prior, sw_basis, name='gp_sw')
deter_sw = solar_wind(n_earth=n_earth)
mean_sw = deterministic_signals.Deterministic(deter_sw, name='n_earth')
sw_model = mean_sw + gp_sw
if include_dmgp:
# DM GP signals
log10_A_dm = parameter.Uniform(-20, -12)
gamma_dm = parameter.Uniform(0, 7)
dm_basis = utils.createfourierdesignmatrix_dm(nmodes=10,
Tspan=Tspan,
logf=True)
dm_prior = utils.powerlaw(log10_A=log10_A_dm, gamma=gamma_dm)
dmgp = gp_signals.BasisGP(dm_prior, dm_basis, name='dm_gp')
sw_model += dmgp
return sw_model
######################
## ipta DR2 model ##
######################
bkend = selections.Selection(selections.by_backend)
bkend_NG = selections.Selection(selections.nanograv_backends)
# fix white noise parameters
efac = parameter.Constant()
equad = parameter.Constant()
ecorr = parameter.Constant()
# DMGP parameters and powerlaw
dm_log10_A = parameter.Uniform(-20, -11)
dm_gamma = parameter.Uniform(0, 7)
dm_pl = utils.powerlaw(log10_A=dm_log10_A, gamma=dm_gamma)
dm_basis = utils.createfourierdesignmatrix_dm(nmodes=30, Tspan=Tspan)
# red noise parameters and powerlaw
if args.ul:
rn_log10_A = parameter.LinearExp(-20, -11)
else:
rn_log10_A = parameter.Uniform(-20, -11)
rn_gamma = parameter.Uniform(0, 7)
rn_pl = utils.powerlaw(log10_A=rn_log10_A, gamma=rn_gamma)
# GWB parameters and powerlaw
orf = utils.hd_orf()
if args.ul:
gwb_log10_A = parameter.LinearExp(-18, -12)('gwb_log10_A')
else:
gwb_log10_A = parameter.Uniform(-18, -12)('gwb_log10_A')
