def white_noise_block(vary=False):
"""
Returns the white noise block of the model:
1. EFAC per backend/receiver system
2. EQUAD per backend/receiver system
3. ECORR per backend/receiver system
:param vary:
If set to true we vary these parameters
with uniform priors. Otherwise they are set to constants
with values to be set later.
"""
# define selection by observing backend
selection = selections.Selection(selections.by_backend)
# white noise parameters
if vary:
efac = parameter.Uniform(0.01, 10.0)
equad = parameter.Uniform(-8.5, -5)
ecorr = parameter.Uniform(-8.5, -5)
else:
efac = parameter.Constant()
equad = parameter.Constant()
ecorr = parameter.Constant()
# white noise signals
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)
# combine signals
s = ef + eq + ec
return s
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 ecorr(self,option="by_backend"):
"""
Similar to EFAC and EQUAD, ECORR is a white noise parameter that
describes a correlation between ToAs in a single epoch (observation).
Arzoumanian, Zaven, et al. The Astrophysical Journal 859.1 (2018): 47.
"""
if option not in selections.__dict__.keys():
raise ValueError('ECORR option must be Enterprise selection function \
name')
se=selections.Selection(selections.__dict__[option])
ecorrpr = interpret_white_noise_prior(self.params.ecorr)
ecs = white_signals.EcorrKernelNoise(log10_ecorr=ecorrpr,selection=se)
return ecs
log10_A_gw_1 = parameter.Uniform(-18, -13)('zlog10_A_gw')
gamma_gw_1 = parameter.Constant(13 / 3)('zgamma_gw')
# Second GW parameters
log10_A_gw_2 = parameter.Uniform(-18, -13)('zlog10_A_other_gw')
gamma_gw_2 = parameter.Constant(7 / 3)('zgamma_other_gw')
##### Set up signals #####
# timing model
tm = gp_signals.TimingModel()
# white noise
ef = white_signals.MeasurementNoise(efac=efac, selection=selection)
eq = white_signals.EquadNoise(log10_equad=log10_equad, selection=selection)
ec = white_signals.EcorrKernelNoise(log10_ecorr=log10_ecorr,
selection=selection)
# red noise (powerlaw with 30 frequencies)
pl = utils.powerlaw(log10_A=red_noise_log10_A, gamma=red_noise_gamma)
rn = gp_signals.FourierBasisGP(spectrum=pl, components=30, Tspan=Tspan)
cpl_1 = utils.powerlaw(log10_A=log10_A_gw_1, gamma=gamma_gw_1)
cpl_2 = utils.powerlaw(log10_A=log10_A_gw_2, gamma=gamma_gw_2)
#Common red noise process with no correlations
crn_1 = gp_signals.FourierBasisGP(spectrum=cpl_1,
components=30,
Tspan=Tspan,
name='gw')
crn_2 = gp_signals.FourierBasisGP(spectrum=cpl_2,
components=30,
def white_noise_block(vary=False,
inc_ecorr=False,
gp_ecorr=False,
efac1=False,
select='backend',
name=None):
"""
Returns the white noise block of the model:
1. EFAC per backend/receiver system
2. EQUAD per backend/receiver system
3. ECORR per backend/receiver system
:param vary:
If set to true we vary these parameters
with uniform priors. Otherwise they are set to constants
with values to be set later.
:param inc_ecorr:
include ECORR, needed for NANOGrav channelized TOAs
:param gp_ecorr:
whether to use the Gaussian process model for ECORR
:param efac1:
use a strong prior on EFAC = Normal(mu=1, stdev=0.1)
"""
if select == 'backend':
# define selection by observing backend
backend = selections.Selection(selections.by_backend)
# define selection by nanograv backends
backend_ng = selections.Selection(selections.nanograv_backends)
else:
# define no selection
backend = selections.Selection(selections.no_selection)
# white noise parameters
if vary:
if efac1:
efac = parameter.Normal(1.0, 0.1)
else:
efac = parameter.Uniform(0.01, 10.0)
equad = parameter.Uniform(-8.5, -5)
if inc_ecorr:
ecorr = parameter.Uniform(-8.5, -5)
else:
efac = parameter.Constant()
equad = parameter.Constant()
if inc_ecorr:
ecorr = parameter.Constant()
# white noise signals
ef = white_signals.MeasurementNoise(efac=efac,
selection=backend,
name=name)
eq = white_signals.EquadNoise(log10_equad=equad,
selection=backend,
name=name)
if inc_ecorr:
if gp_ecorr:
if name is None:
ec = gp_signals.EcorrBasisModel(log10_ecorr=ecorr,
selection=backend_ng)
else:
ec = gp_signals.EcorrBasisModel(log10_ecorr=ecorr,
selection=backend_ng,
name=name)
else:
ec = white_signals.EcorrKernelNoise(log10_ecorr=ecorr,
selection=backend_ng,
name=name)
# combine signals
if inc_ecorr:
s = ef + eq + ec
elif not inc_ecorr:
s = ef + eq
return s
def test_single_pulsar(self):
# get parameters from PAL2 style noise files
params = get_noise_from_pal2(datadir + "/B1855+09_noise.txt")
# setup basic model
efac = parameter.Constant()
equad = parameter.Constant()
ecorr = parameter.Constant()
log10_A = parameter.Constant()
gamma = parameter.Constant()
selection = Selection(selections.by_backend)
ms = white_signals.MeasurementNoise(efac=efac,
log10_t2equad=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)
s = ms + ec + rn
m = s(self.psrs[0])
# set parameters
m.set_default_params(params)
# get parameters
efacs = [params[key] for key in sorted(params.keys()) if "efac" in key]
equads = [
params[key] for key in sorted(params.keys()) if "equad" in key
]
ecorrs = [
params[key] for key in sorted(params.keys()) if "ecorr" in key
]
log10_A = params["B1855+09_red_noise_log10_A"]
gamma = params["B1855+09_red_noise_gamma"]
# correct value
flags = ["430_ASP", "430_PUPPI", "L-wide_ASP", "L-wide_PUPPI"]
nvec0 = np.zeros_like(self.psrs[0].toas)
for ct, flag in enumerate(np.unique(flags)):
ind = flag == self.psrs[0].backend_flags
nvec0[ind] = efacs[ct]**2 * (
self.psrs[0].toaerrs[ind]**2 +
10**(2 * equads[ct]) * np.ones(np.sum(ind)))
# get the basis
bflags = self.psrs[0].backend_flags
Umats = []
for flag in np.unique(bflags):
mask = bflags == flag
Umats.append(
utils.create_quantization_matrix(self.psrs[0].toas[mask])[0])
nepoch = sum(U.shape[1] for U in Umats)
U = np.zeros((len(self.psrs[0].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
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])))
# test
msg = "EFAC/ECORR logdet incorrect."
N = m.get_ndiag(params)
assert np.allclose(N.solve(self.psrs[0].residuals, logdet=True)[1],
logdet,
rtol=1e-10), msg
msg = "EFAC/ECORR D1 solve incorrect."
assert np.allclose(N.solve(self.psrs[0].residuals),
sl.cho_solve(cf, self.psrs[0].residuals),
rtol=1e-10), msg
msg = "EFAC/ECORR 1D1 solve incorrect."
assert np.allclose(
N.solve(self.psrs[0].residuals, left_array=self.psrs[0].residuals),
np.dot(self.psrs[0].residuals,
sl.cho_solve(cf, self.psrs[0].residuals)),
rtol=1e-10,
), msg
msg = "EFAC/ECORR 2D1 solve incorrect."
T = m.get_basis(params)
assert np.allclose(
N.solve(self.psrs[0].residuals, left_array=T),
np.dot(T.T, sl.cho_solve(cf, self.psrs[0].residuals)),
rtol=1e-10,
), msg
msg = "EFAC/ECORR 2D2 solve incorrect."
assert np.allclose(N.solve(T, left_array=T),
np.dot(T.T, sl.cho_solve(cf, T)),
rtol=1e-10), msg
F, f2 = utils.createfourierdesignmatrix_red(self.psrs[0].toas,
nmodes=20)
# spectrum test
phi = utils.powerlaw(f2, log10_A=log10_A, gamma=gamma)
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
def test_pta(self):
# 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)
# setup basic model
efac = parameter.Constant()
equad = parameter.Constant()
ecorr = parameter.Constant()
log10_A = parameter.Constant()
gamma = parameter.Constant()
selection = Selection(selections.by_backend)
ms = white_signals.MeasurementNoise(efac=efac,
log10_t2equad=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)
s = ms + ec + rn
pta = s(self.psrs[0]) + s(self.psrs[1])
# set parameters
pta.set_default_params(params)
# get parameters
efacs, equads, ecorrs, log10_A, gamma = [], [], [], [], []
for pname in [p.name for p in self.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)])
# correct value
tflags = [sorted(list(np.unique(p.backend_flags))) for p in self.psrs]
cfs, logdets, phis = [], [], []
for ii, (psr, flags) in enumerate(zip(self.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 +
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)
phi = utils.powerlaw(f2, log10_A=log10_A[ii], gamma=gamma[ii])
phis.append(phi)
# tests
Ns = pta.get_ndiag(params)
pphis = pta.get_phi(params)
pphiinvs = pta.get_phiinv(params)
Ts = pta.get_basis(params)
zipped = zip(logdets, cfs, phis, self.psrs, Ns, pphis, pphiinvs, Ts)
for logdet, cf, phi, psr, N, pphi, pphiinv, T in zipped:
msg = "EFAC/ECORR logdet incorrect."
assert np.allclose(N.solve(psr.residuals, logdet=True)[1],
logdet,
rtol=1e-10), msg
msg = "EFAC/ECORR D1 solve incorrect."
assert np.allclose(N.solve(psr.residuals),
sl.cho_solve(cf, psr.residuals),
rtol=1e-10), msg
msg = "EFAC/ECORR 1D1 solve incorrect."
assert np.allclose(
N.solve(psr.residuals, left_array=psr.residuals),
np.dot(psr.residuals, sl.cho_solve(cf, psr.residuals)),
rtol=1e-10,
), msg
msg = "EFAC/ECORR 2D1 solve incorrect."
assert np.allclose(N.solve(psr.residuals, left_array=T),
np.dot(T.T, sl.cho_solve(cf, psr.residuals)),
rtol=1e-10), msg
msg = "EFAC/ECORR 2D2 solve incorrect."
assert np.allclose(N.solve(T, left_array=T),
np.dot(T.T, sl.cho_solve(cf, T)),
rtol=1e-10), msg
# spectrum test
msg = "Spectrum incorrect for GP Fourier signal."
assert np.all(pphi == phi), msg
# inverse spectrum test
msg = "Spectrum inverse incorrect for GP Fourier signal."
assert np.all(pphiinv == 1 / phi), msg
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
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 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
rn_gamma = parameter.Uniform(0, 7)
rn_pl = utils.powerlaw(log10_A=rn_log10_A, gamma=rn_gamma)
# GWB parameters and powerlaw
orf = utils.hd_orf()
if args.ul:
gwb_log10_A = parameter.LinearExp(-18, -12)('gwb_log10_A')
else:
gwb_log10_A = parameter.Uniform(-18, -12)('gwb_log10_A')
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,
