def test_gp_parameter(self):
"""Test GP basis model with parameterized basis."""
pl = utils.powerlaw(log10_A=parameter.Uniform(-18, -12),
gamma=parameter.Uniform(0, 7))
basis_env = utils.createfourierdesignmatrix_env(
log10_Amp=parameter.Uniform(-10, -5),
t0=parameter.Uniform(4.3e9, 5e9),
log10_Q=parameter.Uniform(0, 4))
basis_red = utils.createfourierdesignmatrix_red()
rn_env = gp_signals.BasisGP(pl, basis_env, name="env")
rn = gp_signals.BasisGP(pl, basis_red)
s = rn_env + rn
m = s(self.psr)
# parameters
log10_A, gamma = -14.5, 4.33
log10_A_env, gamma_env = -14.0, 2.5
log10_Amp, log10_Q, t0 = -7.3, np.log10(345), 55000 * 86400
params = {
"B1855+09_log10_A": log10_A,
"B1855+09_gamma": gamma,
"B1855+09_env_log10_A": log10_A_env,
"B1855+09_env_gamma": gamma_env,
"B1855+09_env_log10_Q": log10_Q,
"B1855+09_env_log10_Amp": log10_Amp,
"B1855+09_env_t0": t0,
}
# get basis
Fred, f2_red = utils.createfourierdesignmatrix_red(self.psr.toas,
nmodes=30)
Fenv, f2_env = utils.createfourierdesignmatrix_env(self.psr.toas,
nmodes=30,
log10_Amp=log10_Amp,
log10_Q=log10_Q,
t0=t0)
F = np.hstack((Fenv, Fred))
phi_env = utils.powerlaw(f2_env, log10_A=log10_A_env, gamma=gamma_env)
phi_red = utils.powerlaw(f2_red, log10_A=log10_A, gamma=gamma)
phi = np.concatenate((phi_env, phi_red))
# basis matrix test
msg = "F matrix incorrect for GP Fourier signal."
assert np.allclose(F, m.get_basis(params)), msg
# spectrum test
msg = "Spectrum incorrect for GP Fourier signal."
assert np.all(m.get_phi(params) == phi), msg
# inverse spectrum test
msg = "Spectrum inverse incorrect for GP Fourier signal."
assert np.all(m.get_phiinv(params) == 1 / phi), msg
# test shape
msg = "F matrix shape incorrect"
assert m.get_basis(params).shape == F.shape, msg
def test_kernel(self):
log10_sigma = parameter.Uniform(-10, -5)
log10_lam = parameter.Uniform(np.log10(86400), np.log10(1500 * 86400))
basis = create_quant_matrix(dt=7 * 86400)
prior = se_kernel(log10_sigma=log10_sigma, log10_lam=log10_lam)
se = gp_signals.BasisGP(prior, basis, name="se")
sem = se(self.psr)
# parameters
log10_lam, log10_sigma = 7.4, -6.4
params = {"B1855+09_se_log10_lam": log10_lam, "B1855+09_se_log10_sigma": log10_sigma}
# basis check
U, avetoas = create_quant_matrix(self.psr.toas, dt=7 * 86400)
msg = "Kernel Basis incorrect"
assert np.allclose(U, sem.get_basis(params)), msg
# kernel test
K = se_kernel(avetoas, log10_lam=log10_lam, log10_sigma=log10_sigma)
msg = "Kernel incorrect"
assert np.allclose(K, sem.get_phi(params)), msg
# inverse kernel test
Kinv = np.linalg.inv(K)
msg = "Kernel inverse incorrect"
assert np.allclose(Kinv, sem.get_phiinv(params)), msg
def test_free_spec_prior(self):
"""Test that red noise signal returns correct values."""
# set up signal parameter
pr = gp_priors.free_spectrum(
log10_rho=parameter.Uniform(-10, -4, size=30))
basis = gp_bases.createfourierdesignmatrix_red(nmodes=30)
rn = gp_signals.BasisGP(priorFunction=pr,
basisFunction=basis,
name="red_noise")
rnm = rn(self.psr)
# parameters
rhos = np.random.uniform(-10, -4, size=30)
params = {"B1855+09_red_noise_log10_rho": rhos}
# basis matrix test
F, f2 = gp_bases.createfourierdesignmatrix_red(self.psr.toas,
nmodes=30)
msg = "F matrix incorrect for free spectrum."
assert np.allclose(F, rnm.get_basis(params)), msg
# spectrum test
phi = gp_priors.free_spectrum(f2, log10_rho=rhos)
msg = "Spectrum incorrect for free spectrum."
assert np.all(rnm.get_phi(params) == phi), msg
# inverse spectrum test
msg = "Spectrum inverse incorrect for free spectrum."
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 chromred(self, option="vary"):
"""
This is an generalization of DM noise, with the dependence of Fourier
amplitudes on radio frequency nu as ~ 1/nu^chi, where chi is a free
parameter.
Examples of chi:
- Pulse scattering in the ISM: chi = 4 (Lyne A., Graham-Smith F., 2012,
Pulsar astronomy)
- Refractive propagation: chi = 6.4 (Shannon, R. M., and J. M. Cordes.
MNRAS, 464.2 (2017): 2075-2089).
"""
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])
pl = utils.powerlaw(log10_A=log10_A, gamma=gamma, \
components=self.params.red_general_nfouriercomp)
nfreqs = self.determine_nfreqs(sel_func_name=None)
if option == "vary":
idx = parameter.Uniform(self.params.chrom_idx[0], \
self.params.chrom_idx[1])
else:
idx = option
chr_basis = models.createfourierdesignmatrix_chromatic(
nmodes=nfreqs, Tspan=self.params.Tspan, idx=idx)
chrn = gp_signals.BasisGP(pl, chr_basis, name='chromatic_gp')
return chrn
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 test_kernel_backend(self):
# set up signal parameter
selection = Selection(selections.by_backend)
log10_sigma = parameter.Uniform(-10, -5)
log10_lam = parameter.Uniform(np.log10(86400), np.log10(1500 * 86400))
basis = create_quant_matrix(dt=7 * 86400)
prior = se_kernel(log10_sigma=log10_sigma, log10_lam=log10_lam)
se = gp_signals.BasisGP(prior, basis, selection=selection, name="se")
sem = se(self.psr)
# parameters
log10_sigmas = [-7, -6, -6.4, -8.5]
log10_lams = [8.3, 7.4, 6.8, 5.6]
params = {
"B1855+09_se_430_ASP_log10_lam": log10_lams[0],
"B1855+09_se_430_ASP_log10_sigma": log10_sigmas[0],
"B1855+09_se_430_PUPPI_log10_lam": log10_lams[1],
"B1855+09_se_430_PUPPI_log10_sigma": log10_sigmas[1],
"B1855+09_se_L-wide_ASP_log10_lam": log10_lams[2],
"B1855+09_se_L-wide_ASP_log10_sigma": log10_sigmas[2],
"B1855+09_se_L-wide_PUPPI_log10_lam": log10_lams[3],
"B1855+09_se_L-wide_PUPPI_log10_sigma": log10_sigmas[3],
}
# get the basis
bflags = self.psr.backend_flags
Fmats, fs, phis = [], [], []
for ct, flag in enumerate(np.unique(bflags)):
mask = bflags == flag
U, avetoas = create_quant_matrix(self.psr.toas[mask], dt=7 * 86400)
Fmats.append(U)
fs.append(avetoas)
phis.append(
se_kernel(avetoas,
log10_sigma=log10_sigmas[ct],
log10_lam=log10_lams[ct]))
nf = sum(F.shape[1] for F in Fmats)
U = np.zeros((len(self.psr.toas), nf))
K = sl.block_diag(*phis)
Kinv = np.linalg.inv(K)
nftot = 0
for ct, flag in enumerate(np.unique(bflags)):
mask = bflags == flag
nn = Fmats[ct].shape[1]
U[mask, nftot:nn + nftot] = Fmats[ct]
nftot += nn
msg = "Kernel basis incorrect for backend signal."
assert np.allclose(U, sem.get_basis(params)), msg
# spectrum test
msg = "Kernel incorrect for backend signal."
assert np.allclose(sem.get_phi(params), K), msg
# inverse spectrum test
msg = "Kernel inverse incorrect for backend signal."
assert np.allclose(sem.get_phiinv(params), Kinv), msg
def test_turnover_knee_prior(self):
"""Test that red noise signal returns correct values."""
# set up signal parameter
pr = gp_priors.turnover_knee(
log10_A=parameter.Uniform(-18, -12),
gamma=parameter.Uniform(1, 7),
lfb=parameter.Uniform(-9, -7.5),
lfk=parameter.Uniform(-9, -7.5),
kappa=parameter.Uniform(2.5, 5),
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, lfb = -14.5, 4.33, -8.5
lfk, kappa, delta = -8.5, 3, 0.5
params = {
"B1855+09_red_noise_log10_A": log10_A,
"B1855+09_red_noise_gamma": gamma,
"B1855+09_red_noise_lfb": lfb,
"B1855+09_red_noise_lfk": lfk,
"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.turnover_knee(f2,
log10_A=log10_A,
gamma=gamma,
lfb=lfb,
lfk=lfk,
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 test_adapt_t_process_prior(self):
"""Test that red noise signal returns correct values."""
# set up signal parameter
pr = gp_priors.t_process_adapt(
log10_A=parameter.Uniform(-18, -12),
gamma=parameter.Uniform(1, 7),
alphas_adapt=gp_priors.InvGamma(),
nfreq=parameter.Uniform(5, 25),
)
basis = gp_bases.createfourierdesignmatrix_red(nmodes=30)
rn = gp_signals.BasisGP(priorFunction=pr,
basisFunction=basis,
name="red_noise")
rnm = rn(self.psr)
# parameters
alphas = scipy.stats.invgamma.rvs(1, scale=1, size=1)
log10_A, gamma, nfreq = -15, 4.33, 12
params = {
"B1855+09_red_noise_log10_A": log10_A,
"B1855+09_red_noise_gamma": gamma,
"B1855+09_red_noise_alphas_adapt": alphas,
"B1855+09_red_noise_nfreq": nfreq,
}
# basis matrix test
F, f2 = gp_bases.createfourierdesignmatrix_red(self.psr.toas,
nmodes=30)
msg = "F matrix incorrect for free spectrum."
assert np.allclose(F, rnm.get_basis(params)), msg
# spectrum test
phi = gp_priors.t_process_adapt(f2,
log10_A=log10_A,
gamma=gamma,
alphas_adapt=alphas,
nfreq=nfreq)
msg = "Spectrum incorrect for free spectrum."
assert np.all(rnm.get_phi(params) == phi), msg
# inverse spectrum test
msg = "Spectrum inverse incorrect for free spectrum."
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 chromred(self,option="vary"):
"""
This is an generalization of DM noise, with the dependence of Fourier
amplitudes on radio frequency nu as ~ 1/nu^chi, where chi is a free
parameter.
Examples of chi:
- Pulse scattering in the ISM: chi = 4 (Lyne A., Graham-Smith F., 2012,
Pulsar astronomy)
- Refractive propagation: chi = 6.4 (Shannon, R. M., and J. M. Cordes.
MNRAS, 464.2 (2017): 2075-2089).
"""
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])
option, nfreqs = self.option_nfreqs(option, sel_func_name=None)
if type(option) is str and "turnover" in option:
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)
option_split = option.split("_")
del option_split[option_split.index("turnover")]
option = "_".join(option_split)
if option.isdigit(): option = float(option)
else:
pl = utils.powerlaw(log10_A=log10_A, gamma=gamma, \
components=self.params.red_general_nfouriercomp)
#idx_code = option.split"_").index("idx") + 1
if option=="vary":
idx = parameter.Uniform(self.params.chrom_idx[0], \
self.params.chrom_idx[1])
else:
idx = option
chr_basis = gp_bases.createfourierdesignmatrix_chromatic(nmodes=nfreqs,
Tspan=self.params.Tspan,
idx=idx)
chrn = gp_signals.BasisGP(pl, chr_basis, name='chromatic_gp')
return chrn
def test_powerlaw_genmodes_prior(self):
"""Test that red noise signal returns correct values."""
# set up signal parameter
pr = gp_priors.powerlaw_genmodes(log10_A=parameter.Uniform(-18, -12),
gamma=parameter.Uniform(1, 7))
basis = gp_bases.createfourierdesignmatrix_chromatic(nmodes=30)
rn = gp_signals.BasisGP(priorFunction=pr,
basisFunction=basis,
name="red_noise")
rnm = rn(self.psr)
# parameters
log10_A, gamma = -14.5, 4.33
params = {
"B1855+09_red_noise_log10_A": log10_A,
"B1855+09_red_noise_gamma": gamma
}
# basis matrix test
F, f2 = gp_bases.createfourierdesignmatrix_chromatic(self.psr.toas,
self.psr.freqs,
nmodes=30)
msg = "F matrix incorrect for turnover."
assert np.allclose(F, rnm.get_basis(params)), msg
# spectrum test
phi = gp_priors.powerlaw_genmodes(f2, log10_A=log10_A, gamma=gamma)
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 solar_wind_block(n_earth=None, ACE_prior=False, include_swgp=True,
swgp_prior=None, swgp_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 swgp_prior:
Prior function for solar wind Gaussian process. Default is a power law.
:param swgp_basis:
Basis to be used for solar wind Gaussian process.
Options includes ['powerlaw'.'periodic','sq_exp']
:param Tspan:
Sets frequency sampling f_i = i / Tspan. Default will
use overall time span for individual pulsar. Default is to use 15
frequencies (1/Tspan,15/Tspan).
"""
if n_earth is None and not ACE_prior:
n_earth = parameter.Uniform(0,30)('n_earth')
elif n_earth is None and ACE_prior:
n_earth = ACE_SWEPAM_Parameter()('n_earth')
else:
pass
deter_sw = solar_wind(n_earth=n_earth)
mean_sw = deterministic_signals.Deterministic(deter_sw, name='n_earth')
sw_model = mean_sw
if include_swgp:
if swgp_basis == 'powerlaw':
# dm noise parameters that are common
log10_A_sw = parameter.Uniform(-10,1)
gamma_sw = parameter.Uniform(-2,1)
sw_prior = utils.powerlaw(log10_A=log10_A_sw, gamma=gamma_sw)
if Tspan is not None:
freqs = np.linspace(1/Tspan,30/Tspan,30)
freqs = freqs[1/freqs > 1.5*yr_in_sec]
sw_basis = createfourierdesignmatrix_solar_dm(modes=freqs)
else:
sw_basis = createfourierdesignmatrix_solar_dm(nmodes=15,
Tspan=Tspan)
elif swgp_basis == 'periodic':
# Periodic GP kernel for DM
log10_sigma = parameter.Uniform(-10, -6)
log10_ell = parameter.Uniform(1, 4)
log10_p = parameter.Uniform(-4, 1)
log10_gam_p = parameter.Uniform(-3, 2)
sw_basis = gpk.linear_interp_basis_dm(dt=6*86400)
sw_prior = gpk.periodic_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell,
log10_gam_p=log10_gam_p,
log10_p=log10_p)
elif swgp_basis == 'sq_exp':
# squared-exponential GP kernel for DM
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
sw_basis = gpk.linear_interp_basis_dm(dt=6*86400)
sw_prior = gpk.se_dm_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell)
gp_sw = gp_signals.BasisGP(sw_prior, sw_basis, name='gp_sw')
sw_model += gp_sw
return sw_model
def init_pta(params_all):
"""
Initiate enterprise signal models and enterprise.signals.signal_base.PTA.
"""
ptas = dict.fromkeys(params_all.models)
for ii, params in params_all.models.items():
allpsr_model = params_all.noise_model_obj(psr=params_all.psrs,
params=params)
models = list()
from_par_file = list()
ecorrexists = np.zeros(len(params_all.psrs))
# Including parameters common for all pulsars
if params.tm == 'default':
tm = gp_signals.TimingModel()
elif params.tm == 'ridge_regression':
log10_variance = parameter.Uniform(-20, -10)
basis = scaled_tm_basis()
prior = ridge_prior(log10_variance=log10_variance)
tm = gp_signals.BasisGP(prior, basis, name='ridge')
# Adding common noise terms for all pulsars
# Only those common signals are added that are listed in the noise model
# file, getting Enterprise models from the noise model object.
if 'm_all' in locals():
del m_all
for psp, option in params.common_signals.items():
if 'm_all' in locals():
m_all += getattr(allpsr_model, psp)(option=option)
else:
m_all = tm + getattr(allpsr_model, psp)(option=option)
# Including single pulsar noise models
for pnum, psr in enumerate(params_all.psrs):
singlepsr_model = params_all.noise_model_obj(psr=psr,
params=params)
# Determine if ecorr is mentioned in par file
try:
for key, val in psr.t2pulsar.noisemodel.items():
if key.startswith('ecorr') or key.startswith('ECORR'):
ecorrexists[pnum] = True
except Exception as pint_problem:
print(pint_problem)
ecorrexists[pnum] = False
# Add noise models
if psr.name in params.noisemodel.keys():
noise_model_dict_psr = params.noisemodel[psr.name]
else:
noise_model_dict_psr = params.universal
for psp, option in noise_model_dict_psr.items():
if 'm_sep' in locals():
m_sep += getattr(singlepsr_model, psp)(option=option)
elif 'm_all' in locals():
m_sep = m_all + getattr(singlepsr_model,
psp)(option=option)
else:
m_sep = tm + getattr(singlepsr_model, psp)(option=option)
models.append(m_sep(psr))
del m_sep
pta = signal_base.PTA(models)
if 'noisefiles' in params.__dict__.keys():
noisedict = get_noise_dict(psrlist=[p.name for p in params_all.psrs],\
noisefiles=params.noisefiles)
print('For constant parameters using noise files in PAL2 format')
pta.set_default_params(noisedict)
print('Model',ii,'params (',len(pta.param_names),') in order: ', \
pta.param_names)
if params.opts.mpi_regime != 2:
np.savetxt(params.output_dir + '/pars.txt',
pta.param_names,
fmt='%s')
ptas[ii] = pta
return ptas
# backend selection
selection = selections.Selection(selections.no_selection)
ef = white_signals.MeasurementNoise(efac=efac, selection=selection)
eq = white_signals.EquadNoise(log10_equad=equad, selection=selection)
# red noise
pl = utils.powerlaw(log10_A=parameter.Uniform(-18, -12),
gamma=parameter.Uniform(1, 7))
rn = gp_signals.FourierBasisGP(spectrum=pl, components=30)
# timing model
basis = svd_tm_basis()
prior = tm_prior()
tm = gp_signals.BasisGP(prior, basis)
# combined signal
s = ef + eq + rn + tm
outdirs = ['output_outlier', 'output_no_outlier']
for psr, outdir in zip(psrs, outdirs):
# PTA
pta = signal_base.PTA([s(psr)])
## Set up different outlier models ##
mdls = {}
# emulate Vallisneri and van Haasteren mixture model
def chromatic_noise_block(gp_kernel='nondiag',
psd='powerlaw',
nondiag_kernel='periodic',
prior='log-uniform',
dt=15,
df=200,
idx=4,
include_quadratic=False,
Tspan=None,
name='chrom',
components=30,
coefficients=False):
"""
Returns GP chromatic noise model :
1. Chromatic modeled with user defined PSD with
30 sampling frequencies. Available PSDs are
['powerlaw', 'turnover' 'spectrum']
:param gp_kernel:
Whether to use a diagonal kernel for the GP. ['diag','nondiag']
:param nondiag_kernel:
Which nondiagonal kernel to use for the GP.
['periodic','sq_exp','periodic_rfband','sq_exp_rfband']
:param psd:
PSD to use for common red noise signal. Available options
are ['powerlaw', 'turnover' 'spectrum']
:param prior:
What type of prior to use for amplitudes. ['log-uniform','uniform']
:param dt:
time-scale for linear interpolation basis (days)
:param df:
frequency-scale for linear interpolation basis (MHz)
:param idx:
Index of radio frequency dependence (i.e. DM is 2). Any float will work.
:param include_quadratic:
Whether to include a quadratic fit.
:param name: Name of signal
:param Tspan:
Tspan from which to calculate frequencies for PSD-based GPs.
:param components:
Number of frequencies to use in 'diag' GPs.
:param coefficients:
Whether to keep coefficients of the GP.
"""
if gp_kernel == 'diag':
chm_basis = gpb.createfourierdesignmatrix_chromatic(nmodes=components,
Tspan=Tspan)
if psd in ['powerlaw', 'turnover']:
if prior == 'uniform':
log10_A = parameter.LinearExp(-18, -11)
elif prior == 'log-uniform':
log10_A = parameter.Uniform(-18, -11)
gamma = parameter.Uniform(0, 7)
# PSD
if psd == 'powerlaw':
chm_prior = utils.powerlaw(log10_A=log10_A, gamma=gamma)
elif psd == 'turnover':
kappa = parameter.Uniform(0, 7)
lf0 = parameter.Uniform(-9, -7)
chm_prior = utils.turnover(log10_A=log10_A,
gamma=gamma,
lf0=lf0,
kappa=kappa)
if psd == 'spectrum':
if prior == 'uniform':
log10_rho = parameter.LinearExp(-10, -4, size=components)
elif prior == 'log-uniform':
log10_rho = parameter.Uniform(-10, -4, size=components)
chm_prior = gpp.free_spectrum(log10_rho=log10_rho)
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)
chm_basis = gpk.linear_interp_basis_chromatic(dt=dt * const.day)
chm_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)
chm_basis = gpk.get_tf_quantization_matrix(df=df,
dt=dt * const.day,
dm=True,
idx=idx)
chm_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 kernel for DM
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
chm_basis = gpk.linear_interp_basis_chromatic(dt=dt * const.day,
idx=idx)
chm_prior = gpk.se_dm_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell)
elif nondiag_kernel == 'sq_exp_rfband':
# Sq-Exp GP kernel for Chrom 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,
idx=idx)
dm_prior = gpk.sf_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell,
log10_alpha_wgt=log10_alpha_wgt,
log10_ell2=log10_ell2)
cgp = gp_signals.BasisGP(chm_prior,
chm_basis,
name=name + '_gp',
coefficients=coefficients)
if include_quadratic:
# quadratic piece
basis_quad = chrom.chromatic_quad_basis(idx=idx)
prior_quad = chrom.chromatic_quad_prior()
cquad = gp_signals.BasisGP(prior_quad, basis_quad, name=name + '_quad')
cgp += cquad
return cgp
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
psd='powerlaw',
prior='log-uniform',
Tspan=None,
components=10,
gamma_val=None,
coefficients=False)
n_earth = SW.ACE_SWEPAM_Parameter()('n_earth')
sw = SW.solar_wind(n_earth=n_earth)
mean_sw = deterministic_signals.Deterministic(sw, name='mean_sw')
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
dm_se_basis = models.linear_interp_basis_dm(dt=15 * 86400)
dm_se_prior = models.se_dm_kernel(log10_sigma=log10_sigma, log10_ell=log10_ell)
se = gp_signals.BasisGP(dm_se_prior, dm_se_basis, name='dm_gp')
log10_A_sw = parameter.Uniform(-10, 1)('log10_A_sw')
gamma_sw = parameter.Uniform(-2, 1)('gamma_sw')
dm_sw_basis = SW.createfourierdesignmatrix_solar_dm(nmodes=15, Tspan=None)
dm_sw_prior = utils.powerlaw(log10_A=log10_A_sw, gamma=gamma_sw)
gp_sw = gp_signals.BasisGP(priorFunction=dm_sw_prior,
basisFunction=dm_sw_basis,
name='gp_sw')
sw_models = []
sw_models.append(m + dm_gp1) #Model 0, Just DMGP
sw_models.append(m + mean_sw) #Model 1, Just Deterministic SW
sw_models.append(m + dm_gp2 + mean_sw) #Model 2, DMGP + Deter SW
sw_models.append(m + mean_sw + gp_sw) #Model 3, Deter SW + SW GP
sw_models.append(m + SW.solar_wind_block(ACE_prior=True, include_dmgp=False) +
dm_gp2) #Model 4, All the things
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 compute_like(self, npsrs=1, inc_corr=False, inc_kernel=False):
# get parameters from PAL2 style noise files
params = get_noise_from_pal2(datadir + "/B1855+09_noise.txt")
params2 = get_noise_from_pal2(datadir + "/J1909-3744_noise.txt")
params.update(params2)
psrs = self.psrs if npsrs == 2 else [self.psrs[0]]
if inc_corr:
params.update({"GW_gamma": 4.33, "GW_log10_A": -15.0})
# find the maximum time span to set GW frequency sampling
tmin = [p.toas.min() for p in psrs]
tmax = [p.toas.max() for p in psrs]
Tspan = np.max(tmax) - np.min(tmin)
# setup basic model
efac = parameter.Constant()
equad = parameter.Constant()
ecorr = parameter.Constant()
log10_A = parameter.Constant()
gamma = parameter.Constant()
selection = Selection(selections.by_backend)
ef = white_signals.MeasurementNoise(efac=efac, selection=selection)
eq = white_signals.EquadNoise(log10_equad=equad, selection=selection)
ec = white_signals.EcorrKernelNoise(log10_ecorr=ecorr,
selection=selection)
pl = utils.powerlaw(log10_A=log10_A, gamma=gamma)
rn = gp_signals.FourierBasisGP(pl)
orf = utils.hd_orf()
crn = gp_signals.FourierBasisCommonGP(pl,
orf,
components=20,
name="GW",
Tspan=Tspan)
tm = gp_signals.TimingModel()
log10_sigma = parameter.Uniform(-10, -5)
log10_lam = parameter.Uniform(np.log10(86400), np.log10(1500 * 86400))
basis = create_quant_matrix(dt=7 * 86400)
prior = se_kernel(log10_sigma=log10_sigma, log10_lam=log10_lam)
se = gp_signals.BasisGP(prior, basis, name="se")
# set up kernel stuff
if isinstance(inc_kernel, bool):
inc_kernel = [inc_kernel] * npsrs
if inc_corr:
s = ef + eq + ec + rn + crn + tm
else:
s = ef + eq + ec + rn + tm
models = []
for ik, psr in zip(inc_kernel, psrs):
snew = s + se if ik else s
models.append(snew(psr))
pta = signal_base.PTA(models)
# set parameters
pta.set_default_params(params)
# SE kernel parameters
log10_sigmas, log10_lams = [-7.0, -6.5], [7.0, 6.5]
params.update({
"B1855+09_se_log10_lam": log10_lams[0],
"B1855+09_se_log10_sigma": log10_sigmas[0],
"J1909-3744_se_log10_lam": log10_lams[1],
"J1909-3744_se_log10_sigma": log10_sigmas[1],
})
# get parameters
efacs, equads, ecorrs, log10_A, gamma = [], [], [], [], []
lsig, llam = [], []
for pname in [p.name for p in psrs]:
efacs.append([
params[key] for key in sorted(params.keys())
if "efac" in key and pname in key
])
equads.append([
params[key] for key in sorted(params.keys())
if "equad" in key and pname in key
])
ecorrs.append([
params[key] for key in sorted(params.keys())
if "ecorr" in key and pname in key
])
log10_A.append(params["{}_red_noise_log10_A".format(pname)])
gamma.append(params["{}_red_noise_gamma".format(pname)])
lsig.append(params["{}_se_log10_sigma".format(pname)])
llam.append(params["{}_se_log10_lam".format(pname)])
GW_gamma = 4.33
GW_log10_A = -15.0
# correct value
tflags = [sorted(list(np.unique(p.backend_flags))) for p in psrs]
cfs, logdets, phis, Ts = [], [], [], []
for ii, (ik, psr, flags) in enumerate(zip(inc_kernel, psrs, tflags)):
nvec0 = np.zeros_like(psr.toas)
for ct, flag in enumerate(flags):
ind = psr.backend_flags == flag
nvec0[ind] = efacs[ii][ct]**2 * psr.toaerrs[ind]**2
nvec0[ind] += 10**(2 * equads[ii][ct]) * np.ones(np.sum(ind))
# get the basis
bflags = psr.backend_flags
Umats = []
for flag in np.unique(bflags):
mask = bflags == flag
Umats.append(
utils.create_quantization_matrix(psr.toas[mask])[0])
nepoch = sum(U.shape[1] for U in Umats)
U = np.zeros((len(psr.toas), nepoch))
jvec = np.zeros(nepoch)
netot = 0
for ct, flag in enumerate(np.unique(bflags)):
mask = bflags == flag
nn = Umats[ct].shape[1]
U[mask, netot:nn + netot] = Umats[ct]
jvec[netot:nn + netot] = 10**(2 * ecorrs[ii][ct])
netot += nn
# get covariance matrix
cov = np.diag(nvec0) + np.dot(U * jvec[None, :], U.T)
cf = sl.cho_factor(cov)
logdet = np.sum(2 * np.log(np.diag(cf[0])))
cfs.append(cf)
logdets.append(logdet)
F, f2 = utils.createfourierdesignmatrix_red(psr.toas,
nmodes=20,
Tspan=Tspan)
Mmat = psr.Mmat.copy()
norm = np.sqrt(np.sum(Mmat**2, axis=0))
Mmat /= norm
U2, avetoas = create_quant_matrix(psr.toas, dt=7 * 86400)
if ik:
T = np.hstack((F, Mmat, U2))
else:
T = np.hstack((F, Mmat))
Ts.append(T)
phi = utils.powerlaw(f2, log10_A=log10_A[ii], gamma=gamma[ii])
if inc_corr:
phigw = utils.powerlaw(f2, log10_A=GW_log10_A, gamma=GW_gamma)
else:
phigw = np.zeros(40)
K = se_kernel(avetoas,
log10_sigma=log10_sigmas[ii],
log10_lam=log10_lams[ii])
k = np.diag(
np.concatenate((phi + phigw, np.ones(Mmat.shape[1]) * 1e40)))
if ik:
k = sl.block_diag(k, K)
phis.append(k)
# manually compute loglike
loglike = 0
TNrs, TNTs = [], []
for ct, psr in enumerate(psrs):
TNrs.append(np.dot(Ts[ct].T, sl.cho_solve(cfs[ct], psr.residuals)))
TNTs.append(np.dot(Ts[ct].T, sl.cho_solve(cfs[ct], Ts[ct])))
loglike += -0.5 * (
np.dot(psr.residuals, sl.cho_solve(cfs[ct], psr.residuals)) +
logdets[ct])
TNr = np.concatenate(TNrs)
phi = sl.block_diag(*phis)
if inc_corr:
hd = utils.hd_orf(psrs[0].pos, psrs[1].pos)
phi[len(phis[0]):len(phis[0]) + 40, :40] = np.diag(phigw * hd)
phi[:40, len(phis[0]):len(phis[0]) + 40] = np.diag(phigw * hd)
cf = sl.cho_factor(phi)
phiinv = sl.cho_solve(cf, np.eye(phi.shape[0]))
logdetphi = np.sum(2 * np.log(np.diag(cf[0])))
Sigma = sl.block_diag(*TNTs) + phiinv
cf = sl.cho_factor(Sigma)
expval = sl.cho_solve(cf, TNr)
logdetsigma = np.sum(2 * np.log(np.diag(cf[0])))
loglike -= 0.5 * (logdetphi + logdetsigma)
loglike += 0.5 * np.dot(TNr, expval)
method = ["partition", "sparse", "cliques"]
for mth in method:
eloglike = pta.get_lnlikelihood(params, phiinv_method=mth)
msg = "Incorrect like for npsr={}, phiinv={}".format(npsrs, mth)
assert np.allclose(eloglike, loglike), msg
orf = 'hd'
else:
orf = None
gw = models.common_red_noise_block(psd=args.psd,
prior=prior,
Tspan=Tspan,
orf=orf,
gamma_val=args.gamma_gw,
name='gw')
model += gw
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
dm_basis = linear_interp_basis_dm(dt=15 * 86400)
dm_prior = se_dm_kernel(log10_sigma=log10_sigma, log10_ell=log10_ell)
dm_gp = gp_signals.BasisGP(dm_prior, dm_basis, name='dm_gp')
dm_block = dm_gp
# Make solar wind signals
print('sw_r2p ', args.sw_r2p)
# if isinstance(args.sw_r2p,(float,int)):
# args.sw_r2p = [args.sw_r2p]
if args.sw_r2p_ranges is None:
sw_r2p_ranges = args.sw_r2p
elif len(args.sw_r2p) != len(args.sw_r2p_ranges):
raise ValueError('Number of SW powers must match number of prior ranges!! '
'Set # nonvarying ')
else:
sw_r2p_ranges = args.sw_r2p_ranges
# 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')
gwb_gamma = parameter.Constant(13 / 3)('gwb_gamma')
gwb_pl = utils.powerlaw(log10_A=gwb_log10_A, gamma=gwb_gamma)
# signals
ef = white_signals.MeasurementNoise(efac=efac, selection=bkend)
eq = white_signals.EquadNoise(log10_equad=equad, selection=bkend)
ec = white_signals.EcorrKernelNoise(log10_ecorr=ecorr, selection=bkend_NG)
dmgp = gp_signals.BasisGP(dm_pl, dm_basis, name='dm_gp')
dmexp = models.dm_exponential_dip(tmin=54500, tmax=55000, name='dmexp_1')
dm1yr = models.dm_annual_signal()
rn = gp_signals.FourierBasisGP(spectrum=rn_pl, components=30, Tspan=Tspan)
gwb = gp_signals.FourierBasisCommonGP(gwb_pl,
orf,
components=30,
Tspan=Tspan,
name='gw')
tm = gp_signals.TimingModel(use_svd=True)
be = deterministic_signals.PhysicalEphemerisSignal( # widen prior on jup orbit
use_epoch_toas=True,
jup_orb_elements=parameter.Uniform(-0.1, 0.1, size=6)('jup_orb_elements'))
ptas = {}
all_kwargs = {}
# Periodic GP kernel for DM
log10_sigma = parameter.Uniform(-10, -4.8)
log10_ell = parameter.Uniform(1, 2.4)
log10_p = parameter.Uniform(-2, -1)
log10_gam_p = parameter.Uniform(-2, 2)
dm_basis = gpk.linear_interp_basis_dm(dt=3 * 86400)
dm_prior = gpk.periodic_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell,
log10_gam_p=log10_gam_p,
log10_p=log10_p)
dmgp = gp_signals.BasisGP(dm_prior, dm_basis, name='dm_gp1')
# Periodic GP kernel for DM
log10_sigma2 = parameter.Uniform(-4.8, -3)
log10_ell2 = parameter.Uniform(2.4, 5)
log10_p2 = parameter.Uniform(-2, 2)
log10_gam_p2 = parameter.Uniform(-2, 2)
dm_basis2 = gpk.linear_interp_basis_dm(dt=3 * 86400)
dm_prior2 = gpk.periodic_kernel(log10_sigma=log10_sigma2,
log10_ell=log10_ell2,
log10_gam_p=log10_gam_p2,
log10_p=log10_p2)
dmgp2 = gp_signals.BasisGP(dm_prior2, dm_basis2, name='dm_gp2')
def test_combine_signals(self):
"""Test for combining different signals."""
# set up signal parameter
ecorr = parameter.Uniform(-10, -5)
ec = gp_signals.EcorrBasisModel(log10_ecorr=ecorr)
pl = utils.powerlaw(log10_A=parameter.Uniform(-18, -12), gamma=parameter.Uniform(1, 7))
rn = gp_signals.FourierBasisGP(spectrum=pl, components=30)
log10_sigma = parameter.Uniform(-10, -5)
log10_lam = parameter.Uniform(np.log10(86400), np.log10(1500 * 86400))
basis = create_quant_matrix(dt=7 * 86400)
prior = se_kernel(log10_sigma=log10_sigma, log10_lam=log10_lam)
se = gp_signals.BasisGP(prior, basis, name="se")
ts = gp_signals.TimingModel()
s = ec + rn + ts + se
m = s(self.psr)
# parameters
ecorr = -6.4
log10_A, gamma = -14.5, 4.33
log10_lam, log10_sigma = 7.4, -6.4
params = {
"B1855+09_basis_ecorr_log10_ecorr": ecorr,
"B1855+09_red_noise_log10_A": log10_A,
"B1855+09_red_noise_gamma": gamma,
"B1855+09_se_log10_lam": log10_lam,
"B1855+09_se_log10_sigma": log10_sigma,
}
# combined basis matrix
U = utils.create_quantization_matrix(self.psr.toas)[0]
M = self.psr.Mmat.copy()
norm = np.sqrt(np.sum(M ** 2, axis=0))
M /= norm
F, f2 = utils.createfourierdesignmatrix_red(self.psr.toas, nmodes=30)
U2, avetoas = create_quant_matrix(self.psr.toas, dt=7 * 86400)
T = np.hstack((U, F, M, U2))
# combined prior vector
jvec = 10 ** (2 * ecorr) * np.ones(U.shape[1])
phim = np.ones(self.psr.Mmat.shape[1]) * 1e40
phi = utils.powerlaw(f2, log10_A=log10_A, gamma=gamma)
K = se_kernel(avetoas, log10_lam=log10_lam, log10_sigma=log10_sigma)
phivec = np.concatenate((jvec, phi, phim))
phi = sl.block_diag(np.diag(phivec), K)
phiinv = np.linalg.inv(phi)
# basis matrix test
msg = "Basis matrix incorrect for combined signal."
assert np.allclose(T, m.get_basis(params)), msg
# Kernal test
msg = "Prior matrix incorrect for combined signal."
assert np.allclose(m.get_phi(params), phi), msg
# inverse Kernel test
msg = "Prior matrix inverse incorrect for combined signal."
assert np.allclose(m.get_phiinv(params), phiinv), msg
# test shape
msg = "Basis matrix shape incorrect size for combined signal."
assert m.get_basis(params).shape == T.shape, msg
ptas = {}
all_kwargs = {}
# Periodic GP kernel for DM
log10_sigma = parameter.Uniform(-10, -4.8)
log10_ell = parameter.Uniform(1, 2.4)
log10_p = parameter.Uniform(-2, -1)
log10_gam_p = parameter.Uniform(-2, 2)
dm_basis = gpk.linear_interp_basis_dm(dt=14*86400)
dm_prior = gpk.periodic_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell,
log10_gam_p=log10_gam_p,
log10_p=log10_p)
dmgp = gp_signals.BasisGP(dm_prior, dm_basis, name='dm_gp1')
# Periodic GP kernel for DM
log10_sigma2 = parameter.Uniform(-4.8, -4)
log10_ell2 = parameter.Uniform(2.4, 4)
log10_p2 = parameter.Uniform(-2, 1)
log10_gam_p2 = parameter.Uniform(-2, 2)
dm_basis2 = gpk.linear_interp_basis_dm(dt=14*86400)
dm_prior2 = gpk.periodic_kernel(log10_sigma=log10_sigma2,
log10_ell=log10_ell2,
log10_gam_p=log10_gam_p2,
log10_p=log10_p2)
dmgp2 = gp_signals.BasisGP(dm_prior2, dm_basis2, name='dm_gp2')
orf = 'hd'
else:
orf = None
gw = models.common_red_noise_block(psd=args.psd,
prior=prior,
Tspan=Tspan,
orf=orf,
gamma_val=args.gamma_gw,
name='gw')
model += gw
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
dm_basis = linear_interp_basis_dm(dt=15 * 86400)
dm_prior = se_dm_kernel(log10_sigma=log10_sigma, log10_ell=log10_ell)
dm_gp = gp_signals.BasisGP(dm_prior, dm_basis, name='dm_gp')
dm_block = dm_gp
# Make solar wind signals
print('sw_r2p ', args.sw_r2p)
# if isinstance(args.sw_r2p,(float,int)):
# args.sw_r2p = [args.sw_r2p]
if args.sw_r2p_ranges is None:
sw_r2p_ranges = args.sw_r2p
elif len(args.sw_r2p) != len(args.sw_r2p_ranges):
raise ValueError('Number of SW powers must match number of prior ranges!! '
'Set # nonvarying ')
else:
sw_r2p_ranges = args.sw_r2p_ranges
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
selection_ch = selections.Selection(channelized_backends)
selection = selections.Selection(selections.by_backend)
ef = white_signals.MeasurementNoise(efac=efac, selection=selection)
eq = white_signals.EquadNoise(log10_equad=equad, selection=selection)
ec = white_signals.EcorrKernelNoise(log10_ecorr=ecorr, selection=selection_ch)
# red noise (powerlaw with 5 frequencies)
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
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()
eph = deterministic_signals.PhysicalEphemerisSignal(use_epoch_toas=True)
ptas = {}
all_kwargs = {}
# Periodic GP kernel for DM
log10_sigma = parameter.Uniform(-4.4, -3)
log10_ell = parameter.Uniform(3, 4)
log10_p = parameter.Uniform(-1, 1)
log10_gam_p = parameter.Uniform(-1.5, 1)
dm_basis = gpk.linear_interp_basis_dm(dt=14 * 86400)
dm_prior = gpk.periodic_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell,
log10_gam_p=log10_gam_p,
log10_p=log10_p)
dmgp2 = gp_signals.BasisGP(dm_prior, dm_basis, name='dm_gp2')
@signal_base.function
def chromatic_quad(toas, freqs, quad_coeff=np.ones(3) * 1e-10, idx=4):
"""
Basis for chromatic quadratic function.
:param idx: index of chromatic dependence
:return ret: normalized quadratic basis matrix [Ntoa, 3]
"""
t0 = (toas.max() + toas.min()) / 2
a, b, c = 10**quad_coeff[0], 10**quad_coeff[1], 10**quad_coeff[2]
quad = (a * (toas - t0)**2 + b * (toas - t0) + c) * (1400 / freqs)**idx
