def test_gp_timing_model(self):
"""Test that the timing model signal returns correct values."""
# set up signal parameter
ts = gp_signals.TimingModel()
tm = ts(self.psr)
# basis matrix test
M = self.psr.Mmat.copy()
norm = np.sqrt(np.sum(M ** 2, axis=0))
M /= norm
params = {}
msg = "M matrix incorrect for Timing Model signal."
assert np.allclose(M, tm.get_basis(params)), msg
# Jvec test
phi = np.ones(self.psr.Mmat.shape[1]) * 1e40
msg = "Prior vector incorrect for Timing Model signal."
assert np.all(tm.get_phi(params) == phi), msg
# inverse Jvec test
msg = "Prior vector inverse incorrect for Timing Model signal."
assert np.all(tm.get_phiinv(params) == 1 / phi), msg
# test shape
msg = "M matrix shape incorrect"
assert tm.get_basis(params).shape == self.psr.Mmat.shape, msg
# test unnormed
ts = gp_signals.TimingModel(normed=False)
tm = ts(self.psr)
msg = "Incorrect unnormed timing-model matrix"
assert np.allclose(self.psr.Mmat, tm.get_basis({})), msg
# test prescribed norm
ts = gp_signals.TimingModel(normed=np.ones(self.psr.Mmat.shape[1]))
tm = ts(self.psr)
msg = "Incorrect prescribed-norm timing-model matrix"
assert np.allclose(self.psr.Mmat, tm.get_basis({})), msg
# test svd
ts = gp_signals.TimingModel(use_svd=True)
tm = ts(self.psr)
u, s, v = np.linalg.svd(self.psr.Mmat, full_matrices=False)
msg = "Incorrect SVD timing-model matrix"
assert np.allclose(u, tm.get_basis({})), msg
# test incompatible prescription
self.assertRaises(ValueError, gp_signals.TimingModel, use_svd=True, normed=False)
def test_formalism(self):
# create marginalized model
ef = white_signals.MeasurementNoise(
efac=parameter.Uniform(0.1, 5.0))
tm = gp_signals.TimingModel()
ec = gp_signals.EcorrBasisModel(
log10_ecorr=parameter.Uniform(-10, -5))
pl = utils.powerlaw(log10_A=parameter.Uniform(-18, -12),
gamma=parameter.Uniform(1, 7))
rn = gp_signals.FourierBasisGP(spectrum=pl, components=10)
model = ef + tm + ec + rn
pta = signal_base.PTA([model(self.psr)])
# create hierarchical model
tmc = gp_signals.TimingModel(coefficients=True)
ecc = gp_signals.EcorrBasisModel(log10_ecorr=parameter.Uniform(
-10, -5),
coefficients=True)
rnc = gp_signals.FourierBasisGP(spectrum=pl,
components=10,
coefficients=True)
modelc = ef + tmc + ecc + rnc
ptac = signal_base.PTA([modelc(self.psr)])
ps = {
"B1855+09_efac": 1,
"B1855+09_basis_ecorr_log10_ecorr": -6,
"B1855+09_red_noise_log10_A": -14,
"B1855+09_red_noise_gamma": 3,
}
psc = utils.get_coefficients(pta, ps)
d1 = ptac.get_delay(psc)[0]
d2 = (np.dot(pta.pulsarmodels[0].signals[1].get_basis(ps),
psc["B1855+09_linear_timing_model_coefficients"]) +
np.dot(pta.pulsarmodels[0].signals[2].get_basis(ps),
psc["B1855+09_basis_ecorr_coefficients"]) +
np.dot(pta.pulsarmodels[0].signals[3].get_basis(ps),
psc["B1855+09_red_noise_coefficients"]))
msg = "Implicit and explicit PTA delays are different."
assert np.allclose(d1, d2), msg
l1 = pta.get_lnlikelihood(ps)
l2 = ptac.get_lnlikelihood(psc)
# I don't know how to integrate l2 to match l1...
msg = "Marginal and hierarchical likelihoods should be different."
assert l1 != l2, msg
def test_compare_ecorr_likelihood(self):
"""Compare basis and kernel ecorr methods."""
selection = Selection(selections.nanograv_backends)
ef = white_signals.MeasurementNoise()
ec = white_signals.EcorrKernelNoise(selection=selection)
ec2 = gp_signals.EcorrBasisModel(selection=selection)
tm = gp_signals.TimingModel()
m = ef + ec + tm
m2 = ef + ec2 + tm
pta1 = signal_base.PTA([m(p) for p in self.psrs])
pta2 = signal_base.PTA([m2(p) for p in self.psrs])
params = parameter.sample(pta1.params)
l1 = pta1.get_lnlikelihood(params)
# need to translate some names for EcorrBasis
basis_params = {}
for parname, parval in params.items():
if "log10_ecorr" in parname:
toks = parname.split("_")
basisname = toks[0] + "_basis_ecorr_" + "_".join(toks[1:])
basis_params[basisname] = parval
params.update(basis_params)
l2 = pta2.get_lnlikelihood(params)
msg = "Likelihood mismatch between ECORR methods"
assert np.allclose(l1, l2), msg
def test_gp_timing_model(self):
"""Test that the timing model signal returns correct values."""
# set up signal parameter
ts = gp_signals.TimingModel()
tm = ts(self.psr)
# basis matrix test
M = self.psr.Mmat.copy()
norm = np.sqrt(np.sum(M**2, axis=0))
M /= norm
params = {}
msg = "M matrix incorrect for Timing Model signal."
assert np.allclose(M, tm.get_basis(params)), msg
# Jvec test
phi = np.ones(self.psr.Mmat.shape[1]) * 1e40
msg = "Prior vector incorrect for Timing Model signal."
assert np.all(tm.get_phi(params) == phi), msg
# inverse Jvec test
msg = "Prior vector inverse incorrect for Timing Model signal."
assert np.all(tm.get_phiinv(params) == 1 / phi), msg
# test shape
msg = "M matrix shape incorrect"
assert tm.get_basis(params).shape == self.psr.Mmat.shape, msg
def model_1(psr):
"""
Reads in enterprise Pulsar instance and returns a PTA
instantiated with the standard NANOGrav noise model:
1. EFAC per backend/receiver system
2. EQUAD per backend/receiver system
3. ECORR per backend/receiver system
4. Red noise modeled as a power-law with 30 sampling frequencies
5. Linear timing model.
"""
# white noise
s = white_noise_block(vary=True)
# red noise
s += red_noise_block()
# timing model
s += gp_signals.TimingModel()
# set up PTA of one
pta = signal_base.PTA([s(psr)])
return pta
def __init__(self, psrs, params=None):
print('Initializing the model...')
efac = parameter.Constant()
equad = parameter.Constant()
ef = white_signals.MeasurementNoise(efac=efac)
eq = white_signals.EquadNoise(log10_equad=equad)
tm = gp_signals.TimingModel(use_svd=True)
s = eq + ef + tm
model = []
for p in psrs:
model.append(s(p))
self.pta = signal_base.PTA(model)
# set white noise parameters
if params is None:
print('No noise dictionary provided!...')
else:
self.pta.set_default_params(params)
self.psrs = psrs
self.params = params
self.Nmats = None
def get_All_results():
# Modeling each pulsar.
tm = gp_signals.TimingModel()
wnb = models.white_noise_block(vary=True)
dmn = models.dm_noise_block(components=30)
spn = models.red_noise_block(components=30)
model = tm + wnb + dmn + spn
ptas = [signal_base.PTA(model(psr)) for psr in psrs]
# Multiprocessing.
jobs = []
RETs={}
for i in range(len(psrs)):
RETs[i] = multiprocessing.Manager().Value('i',0)
p = multiprocessing.Process(target=get_pulsar_noise, args=(ptas[i],RETs[i]))
jobs.append(p)
p.start()
for p in jobs:
p.join()
# Return the sum of the Ln Maximal Likelihood values.
MLHselect = [RET.value for RET in RETs.values()]
return MLHselect
def test_pshift_fourier(self):
"""Test Fourier basis with prescribed phase shifts."""
# build a SignalCollection with timing model and red noise with phase shifts
Tspan = self.psr.toas.max() - self.psr.toas.min()
pl = utils.powerlaw(log10_A=parameter.Uniform(-18, -12), gamma=parameter.Uniform(0, 7))
ts = gp_signals.TimingModel()
rn = gp_signals.FourierBasisGP(pl, components=5, Tspan=Tspan, pseed=parameter.Uniform(0, 32768))
s = ts + rn
m = s(self.psr)
b1 = m.signals[1].get_basis()
b2 = utils.createfourierdesignmatrix_red(nmodes=5, Tspan=Tspan)("")(self.psr.toas)[0]
msg = "Fourier bases incorrect (no phase shifts)"
assert np.all(b1 == b2), msg
b1 = m.signals[1].get_basis()
b2 = utils.createfourierdesignmatrix_red(nmodes=5, Tspan=Tspan, pseed=5)("")(self.psr.toas)[0]
msg = "Fourier bases incorrect (no-parameter call vs phase shift 5)"
assert not np.all(b1 == b2), msg
b1 = m.signals[1].get_basis(params={self.psr.name + "_red_noise_pseed": 5})
b2 = utils.createfourierdesignmatrix_red(nmodes=5, Tspan=Tspan, pseed=5)("")(self.psr.toas)[0]
msg = "Fourier bases incorrect (phase shift 5)"
assert np.all(b1 == b2), msg
b1 = m.signals[1].get_basis(params={self.psr.name + "_red_noise_pseed": 5})
b2 = utils.createfourierdesignmatrix_red(nmodes=5, Tspan=Tspan)("")(self.psr.toas)[0]
msg = "Fourier bases incorrect (phase-shift-5 call vs no phase shift)"
assert not np.all(b1 == b2), msg
def __init__(self, psrs, params=None,
psrTerm=True, bayesephem=True, pta=None):
if pta is None:
# initialize standard model with fixed white noise
# and powerlaw red noise
# uses the implementation of ECORR in gp_signals
print('Initializing the model...')
tmin = np.min([p.toas.min() for p in psrs])
tmax = np.max([p.toas.max() for p in psrs])
Tspan = tmax - tmin
s = deterministic.cw_block_circ(amp_prior='log-uniform',
psrTerm=psrTerm, tref=tmin, name='cw')
s += gp_signals.TimingModel()
s += blocks.red_noise_block(prior='log-uniform', psd='powerlaw',
Tspan=Tspan, components=30)
if bayesephem:
s += deterministic_signals.PhysicalEphemerisSignal(use_epoch_toas=True)
# adding white-noise, and acting on psr objects
models = []
for p in psrs:
if 'NANOGrav' in p.flags['pta']:
s2 = s + blocks.white_noise_block(vary=False, inc_ecorr=True,
gp_ecorr=True)
models.append(s2(p))
else:
s3 = s + blocks.white_noise_block(vary=False, inc_ecorr=False)
models.append(s3(p))
pta = signal_base.PTA(models)
# set white noise parameters
if params is None:
print('No noise dictionary provided!')
else:
pta.set_default_params(params)
self.pta = pta
else:
# user can specify their own pta object
# if ECORR is included, use the implementation in gp_signals
self.pta = pta
self.psrs = psrs
self.params = params
self.Nmats = self.get_Nmats()
def test_vector_parameter_like(self):
"""Test vector parameter in a likelihood"""
# white noise
efac = parameter.Uniform(0.5, 2)
ef = white_signals.MeasurementNoise(efac=efac)
# red noise
nf = 3
spec = free_spectrum(log10_rho=parameter.Uniform(-20, -10, size=nf))
rn = gp_signals.FourierBasisGP(spec, components=nf)
# timing model
tm = gp_signals.TimingModel()
# combined signal
s = ef + rn + tm
# PTA
pta = signal_base.PTA([s(self.psr)])
# parameters
xs = np.hstack(p.sample() for p in pta.params)
params = {
"B1855+09_red_noise_log10_rho": xs[1:],
"B1855+09_efac": xs[0]
}
# test log likelihood
msg = "Likelihoods do not match"
assert pta.get_lnlikelihood(xs) == pta.get_lnlikelihood(params), msg
# test log prior
msg = "Priors do not match"
assert pta.get_lnprior(xs) == pta.get_lnprior(params), msg
# test prior value
prior = 1 / (2 - 0.5) * (1 / 10)**3
msg = "Prior value incorrect."
assert np.allclose(pta.get_lnprior(xs), np.log(prior)), msg
# test PTA level parameter names
pnames = [
"B1855+09_efac",
"B1855+09_red_noise_log10_rho_0",
"B1855+09_red_noise_log10_rho_1",
"B1855+09_red_noise_log10_rho_2",
]
msg = "Incorrect parameter names"
assert pta.param_names == pnames
def initialize_pta_sim(psrs, fgw):
# continuous GW signal
s = models.cw_block_circ(log10_fgw=np.log10(fgw), psrTerm=True)
# white noise
efac = parameter.Constant(1.0)
s += white_signals.MeasurementNoise(efac=efac)
# linearized timing model
s += gp_signals.TimingModel(use_svd=True)
model = [s(psr) for psr in psrs]
pta = signal_base.PTA(model)
return pta
def add_timingmodel(self):
"""Return dictionary containing timing model signal attributes
:return: OrderedDict of timing model signal
"""
tm = gp_signals.TimingModel(use_svd=False)
npars = self.psr.Mmat.shape[1]
newsignal = OrderedDict({
'type': 'timingmodel',
'name': 'timingmodel',
'pmin': [-1.0e6] * npars,
'pmax': [1.0e6] * npars,
'pstart': [1.0e-10] * npars,
'interval': [False] * npars,
'numpars': npars
})
self.tm_sig = tm(self.psr)
return {'timingmodel': newsignal}
def initialize_pta_sim(psrs, fgw,
inc_efac=True, inc_equad=False, inc_ecorr=False,
selection=None,
inc_red_noise=False, noisedict=None):
# continuous GW signal
s = models.cw_block_circ(log10_fgw=np.log10(fgw), psrTerm=True)
# linearized timing model
s += gp_signals.TimingModel(use_svd=True)
# white noise
if selection == 'backend':
selection = selections.Selection(selections.by_backend)
if inc_efac:
efac = parameter.Constant()
s += white_signals.MeasurementNoise(efac=efac, selection=selection)
if inc_equad:
equad = parameter.Constant()
s += white_signals.EquadNoise(log10_equad=equad,
selection=selection)
if inc_ecorr:
ecorr = parameter.Constant()
s += gp_signals.EcorrBasisModel(log10_ecorr=ecorr,
selection=selection)
if inc_red_noise:
log10_A = parameter.Constant()
gamma = parameter.Constant()
pl = utils.powerlaw(log10_A=log10_A, gamma=gamma)
s += gp_signals.FourierBasisGP(pl, components=30)
model = [s(psr) for psr in psrs]
pta = signal_base.PTA(model)
# set white noise parameters
if noisedict is None:
print('No noise dictionary provided!...')
else:
pta.set_default_params(noisedict)
return pta
def pta_pshift(dmx_psrs, caplog):
Tspan = model_utils.get_tspan(dmx_psrs)
tm = gp_signals.TimingModel()
wn = blocks.white_noise_block(inc_ecorr=True, tnequad=True)
rn = blocks.red_noise_block(Tspan=Tspan)
pseed = parameter.Uniform(0, 10000)('gw_pseed')
gw_log10_A = parameter.Uniform(-18, -14)('gw_log10_A')
gw_gamma = parameter.Constant(13. / 3)('gw_gamma')
gw_pl = utils.powerlaw(log10_A=gw_log10_A, gamma=gw_gamma)
gw_pshift = gp_signals.FourierBasisGP(spectrum=gw_pl,
components=5,
Tspan=Tspan,
name='gw',
pshift=True,
pseed=pseed)
model = tm + wn + rn + gw_pshift
pta_pshift = signal_base.PTA([model(p) for p in dmx_psrs])
pta_pshift.set_default_params(noise_dict)
return pta_pshift
def test_model_2a_altpol_spectrum(nodmx_psrs, caplog):
log10_A_tt = parameter.LinearExp(-18, -12)('log10_A_tt')
log10_A_st = parameter.LinearExp(-18, -12)('log10_A_st')
log10_A_vl = parameter.LinearExp(-18, -15)('log10_A_vl')
log10_A_sl = parameter.LinearExp(-18, -16)('log10_A_sl')
kappa = parameter.Uniform(0, 15)('kappa')
p_dist = parameter.Normal(1.0, 0.2)
pl = model_orfs.generalized_gwpol_psd(log10_A_tt=log10_A_tt,
log10_A_st=log10_A_st,
log10_A_vl=log10_A_vl,
log10_A_sl=log10_A_sl,
kappa=kappa,
p_dist=p_dist,
alpha_tt=-2 / 3,
alpha_alt=-1)
s = models.white_noise_block(vary=False, inc_ecorr=True)
s += models.red_noise_block(prior='log-uniform')
s += gp_signals.FourierBasisGP(spectrum=pl, name='gw')
s += gp_signals.TimingModel()
m = signal_base.PTA([s(psr) for psr in nodmx_psrs])
m.set_default_params(noise_dict)
for param in m.params:
if 'gw_p_dist' in str(param):
# get pulsar name and distance
psr_name = str(param).split('_')[0].strip('"')
psr_dist = [p._pdist for p in nodmx_psrs if psr_name in p.name][0]
# edit prior settings
param._prior = parameter.Normal(mu=psr_dist[0], sigma=psr_dist[1])
param._mu = psr_dist[0]
param._sigma = psr_dist[1]
assert hasattr(m, 'get_lnlikelihood')
def _ecorr_test(self, method="sparse"):
"""Test of sparse/sherman-morrison ecorr signal and solve methods."""
selection = Selection(selections.by_backend)
efac = parameter.Uniform(0.1, 5)
ecorr = parameter.Uniform(-10, -5)
ef = white_signals.MeasurementNoise(efac=efac, selection=selection)
ec = white_signals.EcorrKernelNoise(log10_ecorr=ecorr,
selection=selection,
method=method)
tm = gp_signals.TimingModel()
s = ef + ec + tm
m = s(self.psr)
# set parameters
efacs = [1.3, 1.4, 1.5, 1.6]
ecorrs = [-6.1, -6.2, -6.3, -6.4]
params = {
"B1855+09_430_ASP_efac": efacs[0],
"B1855+09_430_PUPPI_efac": efacs[1],
"B1855+09_L-wide_ASP_efac": efacs[2],
"B1855+09_L-wide_PUPPI_efac": efacs[3],
"B1855+09_430_ASP_log10_ecorr": ecorrs[0],
"B1855+09_430_PUPPI_log10_ecorr": ecorrs[1],
"B1855+09_L-wide_ASP_log10_ecorr": ecorrs[2],
"B1855+09_L-wide_PUPPI_log10_ecorr": ecorrs[3],
}
# get EFAC Nvec
flags = ["430_ASP", "430_PUPPI", "L-wide_ASP", "L-wide_PUPPI"]
nvec0 = np.zeros_like(self.psr.toas)
for ct, flag in enumerate(np.unique(flags)):
ind = flag == self.psr.backend_flags
nvec0[ind] = efacs[ct]**2 * self.psr.toaerrs[ind]**2
# get the basis
bflags = self.psr.backend_flags
Umats = []
for flag in np.unique(bflags):
mask = bflags == flag
Umats.append(
utils.create_quantization_matrix(self.psr.toas[mask],
nmin=2)[0])
nepoch = sum(U.shape[1] for U in Umats)
U = np.zeros((len(self.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[ct])
netot += nn
# get covariance matrix
wd = Woodbury(nvec0, U, jvec)
# test
msg = "EFAC/ECORR {} logdet incorrect.".format(method)
N = m.get_ndiag(params)
assert np.allclose(N.solve(self.psr.residuals, logdet=True)[1],
wd.logdet(),
rtol=1e-10), msg
msg = "EFAC/ECORR {} D1 solve incorrect.".format(method)
assert np.allclose(N.solve(self.psr.residuals),
wd.solve(self.psr.residuals),
rtol=1e-10), msg
msg = "EFAC/ECORR {} 1D1 solve incorrect.".format(method)
assert np.allclose(
N.solve(self.psr.residuals, left_array=self.psr.residuals),
np.dot(self.psr.residuals, wd.solve(self.psr.residuals)),
rtol=1e-10,
), msg
msg = "EFAC/ECORR {} 2D1 solve incorrect.".format(method)
T = m.get_basis()
assert np.allclose(N.solve(self.psr.residuals, left_array=T),
np.dot(T.T, wd.solve(self.psr.residuals)),
rtol=1e-10), msg
msg = "EFAC/ECORR {} 2D2 solve incorrect.".format(method)
assert np.allclose(N.solve(T, left_array=T),
np.dot(T.T, wd.solve(T)),
rtol=1e-10), msg
def test_conditional_gp(self):
ef = white_signals.MeasurementNoise(efac=parameter.Uniform(0.1, 5.0))
tm = gp_signals.TimingModel()
ec = gp_signals.EcorrBasisModel(log10_ecorr=parameter.Uniform(-10, -5))
pl = utils.powerlaw(log10_A=parameter.Uniform(-18, -12),
gamma=parameter.Uniform(1, 7))
rn = gp_signals.FourierBasisGP(spectrum=pl,
components=10,
combine=False)
model = ef + tm + ec + rn
pta = signal_base.PTA([model(self.psr), model(self.psr2)])
p0 = {
"B1855+09_basis_ecorr_log10_ecorr": -6.051740765663904,
"B1855+09_efac": 2.9027266737466095,
"B1855+09_red_noise_gamma": 6.9720332277819725,
"B1855+09_red_noise_log10_A": -16.749192700991543,
"B1937+21_basis_ecorr_log10_ecorr": -9.726747733721872,
"B1937+21_efac": 3.959178240268702,
"B1937+21_red_noise_gamma": 2.9030772884814797,
"B1937+21_red_noise_log10_A": -17.978562921948992,
}
c = utils.ConditionalGP(pta)
cmean = c.get_mean_coefficients(p0)
# build index for the global coefficient vector
idx, ntot = {}, 0
for l, v in cmean.items():
idx[l] = slice(ntot, ntot + len(v))
ntot = ntot + len(v)
# repeat the computation using the common-signal formalism
TNrs = pta.get_TNr(p0)
TNTs = pta.get_TNT(p0)
phiinvs = pta.get_phiinv(p0, logdet=False, method="cliques")
TNr = np.concatenate(TNrs)
Sigma = sps.block_diag(TNTs, "csc") + sps.block_diag(
[np.diag(phiinvs[0]), np.diag(phiinvs[1])])
ch = cholesky(Sigma)
mn = ch(TNr)
iSigma = sps.linalg.inv(Sigma)
# check mean values
msg = "Conditional GP coefficient value does not match"
for l, v in cmean.items():
assert np.allclose(mn[idx[l]], v, atol=1e-4, rtol=1e-4), msg
# check variances
par = "B1937+21_linear_timing_model_coefficients"
c1 = np.cov(
np.array([cs[par] for cs in c.sample_coefficients(p0, n=10000)]).T)
c2 = iSigma[idx[par], idx[par]].toarray().T
msg = "Conditional GP coefficient variance does not match"
assert np.allclose(c1, c2, atol=1e-4, rtol=1e-4), msg
# check mean processes
proc = "B1937+21_linear_timing_model"
p1 = c.get_mean_processes(p0)[proc]
p2 = np.dot(pta["B1937+21"]["linear_timing_model"].get_basis(),
mn[idx[par]])
msg = "Conditional GP time series does not match"
assert np.allclose(p1, p2, atol=1e-4, rtol=1e-4), msg
# check mean of sampled processes
p2 = np.mean(np.array(
[pc[proc] for pc in c.sample_processes(p0, n=1000)]),
axis=0)
msg = "Mean of sampled conditional GP processes does not match"
assert np.allclose(p1, p2, atol=1e-4, rtol=1e-4)
# now try with a common process
crn = gp_signals.FourierBasisCommonGP(spectrum=pl,
orf=utils.hd_orf(),
components=10,
combine=False)
model = ef + tm + ec + crn
pta = signal_base.PTA([model(self.psr), model(self.psr2)])
p0 = {
"B1855+09_basis_ecorr_log10_ecorr": -5.861847220080768,
"B1855+09_efac": 4.588342210948306,
"B1937+21_basis_ecorr_log10_ecorr": -9.151872649912377,
"B1937+21_efac": 0.8947815819783302,
"common_fourier_gamma": 6.638289750637263,
"common_fourier_log10_A": -15.68180643904114,
}
c = utils.ConditionalGP(pta)
cmean = c.get_mean_coefficients(p0)
idx, ntot = {}, 0
for l, v in cmean.items():
idx[l] = slice(ntot, ntot + len(v))
ntot = ntot + len(v)
TNrs = pta.get_TNr(p0)
TNTs = pta.get_TNT(p0)
phiinvs = pta.get_phiinv(p0, logdet=False, method="cliques")
TNr = np.concatenate(TNrs)
Sigma = sps.block_diag(TNTs, "csc") + sps.csc_matrix(phiinvs)
ch = cholesky(Sigma)
mn = ch(TNr)
msg = "Conditional GP coefficient value does not match for common GP"
for l, v in cmean.items():
assert np.allclose(mn[idx[l]], v)
def gwb_ul(psrs_cut, num_points):
# find the maximum time span to set GW frequency sampling
tmin = [p.toas.min() for p in psrs_cut]
tmax = [p.toas.max() for p in psrs_cut]
Tspan = np.max(tmax) - np.min(tmin)
# define selection by observing backend
selection = selections.Selection(selections.by_backend)
# white noise parameters
# we set these ourselves so we know the most likely values!
efac = parameter.Constant(1)
# quad = parameter.Constant(0)
# ecorr = parameter.Constant(0)
# red noise parameters
log10_A = parameter.LinearExp(-20, -11)
gamma = parameter.Uniform(0, 7)
# GW parameters (initialize with names here to use parameters in common across pulsars)
log10_A_gw = parameter.LinearExp(-18, -12)('log10_A_gw')
gamma_gw = parameter.Constant(4.33)('gamma_gw')
# white noise
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)
# red noise (powerlaw with 30 frequencies)
pl = utils.powerlaw(log10_A=log10_A, gamma=gamma)
rn = gp_signals.FourierBasisGP(spectrum=pl, components=30, Tspan=Tspan)
# gwb (no spatial correlations)
cpl = utils.powerlaw(log10_A=log10_A_gw, gamma=gamma_gw)
gw = gp_signals.FourierBasisGP(spectrum=cpl,
components=30,
Tspan=Tspan,
name='gw')
# timing model
tm = gp_signals.TimingModel(
use_svd=True) # stabilizing timing model design matrix with SVD
s = ef + rn + gw + tm
# intialize PTA
models = []
for p in psrs_cut:
models.append(s(p))
pta = signal_base.PTA(models)
outDir = './chains/psrs/{0}'.format(psrs_cut[0].name)
sample = sampler.setup_sampler(pta, outdir=outDir)
x0 = np.hstack([p.sample() for p in pta.params])
# sampler for N steps
N = int(
num_points) # normally, we would use 5e6 samples (this will save time)
sample.sample(
x0,
N,
SCAMweight=30,
AMweight=15,
DEweight=50,
)
chain = np.loadtxt(os.path.join(outDir, 'chain_1.txt'))
pars = np.loadtxt(outDir + '/pars.txt', dtype=np.unicode_)
ind = list(pars).index('log10_A_gw')
UL, unc = model_utils.ul(chain[:, ind])
return UL, unc
def model_bwm(psrs,
Tmin_bwm=None,
Tmax_bwm=None,
skyloc=None,
logmin=-18,
logmax=-11,
upper_limit=False,
bayesephem=False,
sngl_psr=False,
dmgp=False,
free_rn=False):
"""
Reads in list of enterprise Pulsar instance and returns a PTA
instantiated with BWM model:
per pulsar:
1. fixed EFAC per backend/receiver system
2. fixed EQUAD per backend/receiver system
3. fixed ECORR per backend/receiver system
4. Red noise modeled as a power-law with 30 sampling frequencies
5. Linear timing model.
global:
1. Deterministic GW burst with memory signal.
2. Optional physical ephemeris modeling.
:param Tmin_bwm:
Min time to search for BWM (MJD). If omitted, uses first TOA.
:param Tmax_bwm:
Max time to search for BWM (MJD). If omitted, uses last TOA.
:param skyloc:
Fixed sky location of BWM signal search as [cos(theta), phi].
Search over sky location if ``None`` given.
:param logmin:
log of minimum BWM amplitude for prior (log10)
:param logmax:
log of maximum BWM amplitude for prior (log10)
:param upper_limit:
Perform upper limit on common red noise amplitude. By default
this is set to False. Note that when perfoming upper limits it
is recommended that the spectral index also be fixed to a specific
value.
:param bayesephem:
Include BayesEphem model. Set to False by default
:param sngl_psr:
run on a single pulsar only. Uses different BWM parameterization to
avoid problem with sky nulls. Set to False by default.
:param free_rn:
Use free red noise spectrum model. Set to False by default.
"""
amp_prior = 'uniform' if upper_limit else 'log-uniform'
# find the maximum time span to set GW frequency sampling
tmin = np.min([p.toas.min() for p in psrs])
tmax = np.max([p.toas.max() for p in psrs])
Tspan = tmax - tmin
if Tmin_bwm == None:
Tmin_bwm = tmin / const.day
if Tmax_bwm == None:
Tmax_bwm = tmax / const.day
# white noise
s = white_noise_block(vary=False)
# red noise
if free_rn:
s += free_noise_block(prior=amp_prior, Tspan=Tspan)
else:
s += red_noise_block(prior=amp_prior, Tspan=Tspan)
# GW BWM signal block
s += bwm_block(Tmin_bwm,
Tmax_bwm,
amp_prior=amp_prior,
skyloc=skyloc,
logmin=logmin,
logmax=logmax,
sngl=sngl_psr,
name='bwm')
# ephemeris model
if bayesephem:
s += deterministic_signals.PhysicalEphemerisSignal(use_epoch_toas=True)
# timing model
s += gp_signals.TimingModel(use_svd=True)
# set up PTA
pta = signal_base.PTA([s(psr) for psr in psrs])
return pta
def model_gwb(psrs,
psd='powerlaw',
gamma_common=None,
orf=None,
upper_limit=False,
bayesephem=False):
"""
Reads in list of enterprise Pulsar instance and returns a PTA
instantiated with GWB model:
per pulsar:
1. fixed EFAC per backend/receiver system
2. fixed EQUAD per backend/receiver system
3. fixed ECORR per backend/receiver system
4. Red noise modeled as a power-law with 30 sampling frequencies
5. Linear timing model.
global:
1.Common red noise modeled with user defined PSD with
30 sampling frequencies. Available PSDs are
['powerlaw', 'turnover']
2. Optional physical ephemeris modeling.
:param psd:
PSD to use for common red noise signal. Available options
are ['powerlaw', 'turnover']. 'powerlaw' is default
value.
:param gamma_common:
Fixed common red process spectral index value. By default we
vary the spectral index over the 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 upper_limit:
Perform upper limit on common red noise amplitude. By default
this is set to False. Note that when perfoming upper limits it
is recommended that the spectral index also be fixed to a specific
value.
:param bayesephem:
Include BayesEphem model. Set to False by default
"""
amp_prior = 'uniform' if upper_limit else 'log-uniform'
# find the maximum time span to set GW frequency sampling
tmin = np.min([p.toas.min() for p in psrs])
tmax = np.max([p.toas.max() for p in psrs])
Tspan = tmax - tmin
# white noise
s = white_noise_block(vary=False)
# red noise
s += red_noise_block(prior=amp_prior, Tspan=Tspan)
# common red noise block
s += common_red_noise_block(psd=psd,
prior=amp_prior,
Tspan=Tspan,
gamma_val=gamma_common,
name='gwb',
orf=orf)
# ephemeris model
if bayesephem:
s += deterministic_signals.PhysicalEphemerisSignal(use_epoch_toas=True)
# timing model
s += gp_signals.TimingModel()
# set up PTA
pta = signal_base.PTA([s(psr) for psr in psrs])
return pta
def model_bwm(psrs,
Tmin_bwm=None,
Tmax_bwm=None,
skyloc=None,
logmin=-18,
logmax=-11,
amp_prior='log-uniform',
bayesephem=False,
dmgp=False,
free_rn=False):
"""
Reads in list of enterprise Pulsar instance and returns a PTA
instantiated with BWM model:
per pulsar:
1. fixed EFAC per backend/receiver system
2. fixed EQUAD per backend/receiver system
3. fixed ECORR per backend/receiver system
4. Red noise modeled as a power-law with 30 sampling frequencies
5. Linear timing model.
global:
1. Deterministic GW burst with memory signal.
2. Optional physical ephemeris modeling.
:param Tmin_bwm:
Min time to search for BWM (MJD). If omitted, uses first TOA.
:param Tmax_bwm:
Max time to search for BWM (MJD). If omitted, uses last TOA.
:param skyloc:
Fixed sky location of BWM signal search as [cos(theta), phi].
Search over sky location if ``None`` given.
:param logmin:
log of minimum BWM amplitude for prior (log10)
:param logmax:
log of maximum BWM amplitude for prior (log10)
:param upper_limit:
Perform upper limit on common red noise amplitude. By default
this is set to False. Note that when perfoming upper limits it
is recommended that the spectral index also be fixed to a specific
value.
:param bayesephem:
Include BayesEphem model. Set to False by default
:param free_rn:
Use free red noise spectrum model. Set to False by default
"""
# find the maximum time span to set GW frequency sampling
tmin = np.min([p.toas.min() for p in psrs])
tmax = np.max([p.toas.max() for p in psrs])
Tspan = tmax - tmin
if Tmin_bwm == None:
Tmin_bwm = tmin / const.day
if Tmax_bwm == None:
Tmax_bwm = tmax / const.day
# white noise
s = models.white_noise_block(vary=False)
# red noise
if free_rn:
s += models.free_noise_block(prior=amp_prior, Tspan=Tspan)
else:
s += red_noise_block(prior=amp_prior, Tspan=Tspan)
# GW BWM signal block
s += bwm_sngl_block(Tmin_bwm,
Tmax_bwm,
amp_prior=amp_prior,
logmin=logmin,
logmax=logmax,
name='bwm')
# ephemeris model
if bayesephem:
s += deterministic_signals.PhysicalEphemerisSignal(use_epoch_toas=True)
# timing model
s += gp_signals.TimingModel(use_svd=True)
# DM variations model
if dmgp:
s += models.dm_noise_block(gp_kernel='diag',
psd='powerlaw',
prior=amp_prior,
Tspan=Tspan)
s += models.dm_annual_signal()
# DM exponential dip for J1713's DM event
dmexp = models.dm_exponential_dip(tmin=54500, tmax=54900)
s2 = s + dmexp
# set up PTA
mods = []
for p in psrs:
if dmgp and 'J1713+0747' == p.name:
mods.append(s2(p))
else:
mods.append(s(p))
pta = signal_base.PTA(mods)
return pta
bwm_log10_A = parameter.LinearExp(-18, -11)(amp_name)
else:
bwm_log10_A = parameter.Uniform(-18, -11)(amp_name)
t0 = parameter.Constant(args.t0)('bwm_t0')
pol = parameter.Constant(args.psi)('bwm_pol')
phi = parameter.Constant(args.phi)('bwm_phi')
costh = parameter.Constant(args.costh)('bwm_costheta')
bwm_wf = utils.bwm_delay(log10_h=bwm_log10_A, t0=t0,
cos_gwtheta=costh, gwphi=phi, gwpol=pol)
# BWM signal
bwm = deterministic_signals.Deterministic(bwm_wf, name='bwm')
# Timing Model
tm = gp_signals.TimingModel(use_svd=True)
# BayesEphem
be = deterministic_signals.PhysicalEphemerisSignal(use_epoch_toas=True)
# construct PTA
mod = tm + wn + rn + bwm
if args.BE:
mod += be
pta = signal_base.PTA([mod(p) for p in psrs])
pta.set_default_params(noise_params)
sumfile = os.path.join(outdir, 'summary.txt')
with open(sumfile, 'w') as f:
f.write(pta.summary())
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
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
pta = signal_base.PTA(model(psr))
x0 = np.hstack(p.sample() for p in pta.params)
def model_simple(psrs, psd='powerlaw', efac=False, n_gwbfreqs=30,
components=30, freqs=None,
vary_gamma=False, upper_limit=False, bayesephem=False,
select='backend', red_noise=False, Tspan=None, hd_orf=False,
rn_dropout=False, dp_threshold=0.5):
"""
Reads in list of enterprise Pulsar instance and returns a PTA
instantiated with the most simple model allowable for enterprise:
per pulsar:
1. fixed EFAC per backend/receiver system at 1.0
2. Linear timing model.
3. Red noise modeled as a power-law with
30 sampling frequencies. Default=False
global:
1.Common red noise modeled with user defined PSD with
30 sampling frequencies. Available PSDs are
['powerlaw', 'turnover' 'spectrum']
2. Optional physical ephemeris modeling.
:param psd:
PSD to use for common red noise signal. Available options
are ['powerlaw', 'turnover' 'spectrum']. 'powerlaw' is default
value.
:param gamma_common:
Fixed common red process spectral index value. By default we
vary the spectral index over the range [0, 7].
:param upper_limit:
Perform upper limit on common red noise amplitude. By default
this is set to False. Note that when performing upper limits it
is recommended that the spectral index also be fixed to a specific
value.
:param bayesephem:
Include BayesEphem model. Set to False by default
"""
amp_prior = 'uniform' if upper_limit else 'log-uniform'
# find the maximum time span to set GW frequency sampling
if Tspan is None:
Tspan = model_utils.get_tspan(psrs)
# timing model
model = gp_signals.TimingModel()
#Only White Noise is EFAC set to 1.0
selection = selections.Selection(selections.by_backend)
if efac:
ef = parameter.Uniform(0.1,10.0)
else:
ef = parameter.Constant(1.00)
model += white_signals.MeasurementNoise(efac=ef, selection=selection)
# common red noise block
if upper_limit:
log10_A_gw = parameter.LinearExp(-18,-12)('gw_log10_A')
else:
log10_A_gw = parameter.Uniform(-18,-12)('gw_log10_A')
if vary_gamma:
gamma_gw = parameter.Uniform(0,7)('gw_gamma')
else:
gamma_gw = parameter.Constant(4.33)('gw_gamma')
pl = signal_base.Function(utils.powerlaw, log10_A=log10_A_gw,
gamma=gamma_gw)
if hd_orf:
if freqs is None:
gw = gp_signals.FourierBasisCommonGP(spectrum=pl,
orf=utils.hd_orf(),
components=n_gwbfreqs,
Tspan=Tspan,
name='gw')
else:
gw = gp_signals.FourierBasisCommonGP(spectrum=pl,
orf=utils.hd_orf(),
modes=freqs,
name='gw')
model += gw
else:
if freqs is None:
crn = gp_signals.FourierBasisGP(spectrum=pl, components=n_gwbfreqs,
Tspan=Tspan, name='gw')
else:
crn = gp_signals.FourierBasisGP(spectrum=pl, modes=freqs,
name='gw')
model += crn
if red_noise and rn_dropout:
if amp_prior == 'uniform':
log10_A = parameter.LinearExp(-20, -11)
elif amp_prior == 'log-uniform':
log10_A = parameter.Uniform(-20, -11)
else:
log10_A = parameter.Uniform(-20, -11)
gamma = parameter.Uniform(0, 7)
k_drop = parameter.Uniform(0, 1)
if dp_threshold == 6.0:
dp_threshold = parameter.Uniform(0,1)('k_threshold')
pl = dropout.dropout_powerlaw(log10_A=log10_A, gamma=gamma,
k_drop=k_drop, k_threshold=dp_threshold)
rn = gp_signals.FourierBasisGP(pl, components=components,
Tspan=Tspan, name='red_noise')
model += rn
elif red_noise:
# red noise
model += models.red_noise_block(prior=amp_prior, Tspan=Tspan,
components=components)
# ephemeris model
if bayesephem:
model += deterministic_signals.PhysicalEphemerisSignal(use_epoch_toas=True)
# set up PTA
pta = signal_base.PTA([model(p) for p in psrs])
return pta
def model_3d(psrs, psd='powerlaw', gamma_common=None, upper_limit=False, bayesephem=False):
"""
Reads in list of enterprise Pulsar instance and returns a PTA
instantiated with model 3D from the analysis paper:
per pulsar:
1. fixed EFAC per backend/receiver system
2. fixed EQUAD per backend/receiver system
3. fixed ECORR per backend/receiver system
4. Red noise modeled as a power-law with 30 sampling frequencies
5. Linear timing model.
global:
1. GWB with HD correlations modeled with user defined PSD with
30 sampling frequencies. Available PSDs are
['powerlaw', 'turnover' 'spectrum']
2. Monopole signal modeled with user defined PSD with
30 sampling frequencies. Available PSDs are
['powerlaw', 'turnover' 'spectrum']
3. Optional physical ephemeris modeling.
:param psd:
PSD to use for common red noise signal. Available options
are ['powerlaw', 'turnover' 'spectrum'] 'powerlaw' is default
value.
:param gamma_common:
Fixed common red process spectral index value. By default we
vary the spectral index over the range [0, 7].
:param upper_limit:
Perform upper limit on common red noise amplitude. By default
this is set to False. Note that when perfoming upper limits it
is recommended that the spectral index also be fixed to a specific
value.
:param bayesephem:
Include BayesEphem model. Set to False by default
"""
amp_prior = 'uniform' if upper_limit else 'log-uniform'
# 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)
# white noise
s = white_noise_block(vary=False)
# red noise
s += red_noise_block(prior=amp_prior, Tspan=Tspan)
# common red noise block
s += common_red_noise_block(psd=psd, prior=amp_prior, Tspan=Tspan,
gamma_val=gamma_common, orf='hd', name='gw')
# monopole
s += common_red_noise_block(psd=psd, prior=amp_prior, Tspan=Tspan,
gamma_val=gamma_common, orf='monopole',
name='monopole')
# ephemeris model
if bayesephem:
s += deterministic_signals.PhysicalEphemerisSignal(use_epoch_toas=True)
# timing model
s += gp_signals.TimingModel()
# set up PTA
pta = signal_base.PTA([s(psr) for psr in psrs])
# set white noise parameters
noisedict = get_noise_dict(psrlist=[p.name for p in psrs])
pta.set_default_params(noisedict)
return pta
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
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
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)
wnb = models.white_noise_block(vary=False)
model = tm + dp + wnb + dmn + spn + eph
nparams = [] # Get the number of parameters of each pulsar
signals = []
for psr in psrs:
signal = model(psr)
nparams.append(len(signal.params) -
5) # Subtracting common DPDM params
signals.append(signal)
PTA = signal_base.PTA(signals)
ndim = len(PTA.params) + 5
# Use the best fit noise parameters!
def _ecorr_test_ipta(self, method="sparse"):
"""Test of sparse/sherman-morrison ecorr signal and solve methods."""
selection = Selection(selections.nanograv_backends)
efac = parameter.Uniform(0.1, 5)
ecorr = parameter.Uniform(-10, -5)
ef = white_signals.MeasurementNoise(efac=efac)
ec = white_signals.EcorrKernelNoise(log10_ecorr=ecorr,
selection=selection,
method=method)
tm = gp_signals.TimingModel()
s = ef + ec + tm
m = s(self.ipsr)
# set parameters
efacs = [1.3]
ecorrs = [-6.1, -6.2, -6.3, -6.4, -7.2, -8.4, -7.1, -7.9]
params = {
"J1713+0747_efac": efacs[0],
"J1713+0747_ASP-L_log10_ecorr": ecorrs[0],
"J1713+0747_ASP-S_log10_ecorr": ecorrs[1],
"J1713+0747_GASP-8_log10_ecorr": ecorrs[2],
"J1713+0747_GASP-L_log10_ecorr": ecorrs[3],
"J1713+0747_GUPPI-8_log10_ecorr": ecorrs[4],
"J1713+0747_GUPPI-L_log10_ecorr": ecorrs[5],
"J1713+0747_PUPPI-L_log10_ecorr": ecorrs[6],
"J1713+0747_PUPPI-S_log10_ecorr": ecorrs[7],
}
# get EFAC Nvec
nvec0 = efacs[0]**2 * self.ipsr.toaerrs**2
# get the basis
flags = [
"ASP-L", "ASP-S", "GASP-8", "GASP-L", "GUPPI-8", "GUPPI-L",
"PUPPI-L", "PUPPI-S"
]
bflags = self.ipsr.backend_flags
Umats = []
for flag in np.unique(bflags):
if flag in flags:
mask = bflags == flag
Umats.append(
utils.create_quantization_matrix(self.ipsr.toas[mask],
nmin=2)[0])
nepoch = sum(U.shape[1] for U in Umats)
U = np.zeros((len(self.ipsr.toas), nepoch))
jvec = np.zeros(nepoch)
netot, ct = 0, 0
for flag in np.unique(bflags):
if flag in flags:
mask = bflags == flag
nn = Umats[ct].shape[1]
U[mask, netot:nn + netot] = Umats[ct]
jvec[netot:nn + netot] = 10**(2 * ecorrs[ct])
netot += nn
ct += 1
# get covariance matrix
wd = Woodbury(nvec0, U, jvec)
# test
msg = "EFAC/ECORR {} logdet incorrect.".format(method)
N = m.get_ndiag(params)
assert np.allclose(N.solve(self.ipsr.residuals, logdet=True)[1],
wd.logdet(),
rtol=1e-8), msg
msg = "EFAC/ECORR {} D1 solve incorrect.".format(method)
assert np.allclose(N.solve(self.ipsr.residuals),
wd.solve(self.ipsr.residuals),
rtol=1e-8), msg
msg = "EFAC/ECORR {} 1D1 solve incorrect.".format(method)
assert np.allclose(
N.solve(self.ipsr.residuals, left_array=self.ipsr.residuals),
np.dot(self.ipsr.residuals, wd.solve(self.ipsr.residuals)),
rtol=1e-8,
), msg
msg = "EFAC/ECORR {} 2D1 solve incorrect.".format(method)
T = m.get_basis()
assert np.allclose(N.solve(self.ipsr.residuals, left_array=T),
np.dot(T.T, wd.solve(self.ipsr.residuals)),
rtol=1e-8), msg
msg = "EFAC/ECORR {} 2D2 solve incorrect.".format(method)
assert np.allclose(N.solve(T, left_array=T),
np.dot(T.T, wd.solve(T)),
rtol=1e-8), msg