def test_fourier_red_noise_pshift(self):
"""Test that red noise signal returns correct values."""
# set up signal parameter
pl = utils.powerlaw(log10_A=parameter.Uniform(-18, -12), gamma=parameter.Uniform(1, 7))
rn = gp_signals.FourierBasisGP(spectrum=pl, components=30, pshift=True, pseed=42)
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 = utils.createfourierdesignmatrix_red(self.psr.toas, nmodes=30, pshift=True, pseed=42)
msg = "F matrix incorrect for GP Fourier signal."
assert np.allclose(F, rnm.get_basis(params)), msg
# spectrum test
phi = utils.powerlaw(f2, log10_A=log10_A, gamma=gamma)
msg = "Spectrum incorrect for GP Fourier signal."
assert np.all(rnm.get_phi(params) == phi), msg
# inverse spectrum test
msg = "Spectrum inverse incorrect for GP Fourier signal."
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_fourier_red_user_freq_array(self):
"""Test that red noise signal returns correct values with user defined
frequency array."""
# set parameters
log10_A, gamma = -14.5, 4.33
params = {"B1855+09_red_noise_log10_A": log10_A, "B1855+09_red_noise_gamma": gamma}
F, f2 = utils.createfourierdesignmatrix_red(self.psr.toas, nmodes=30)
# set up signal model. use list of frequencies to make basis
pl = utils.powerlaw(log10_A=parameter.Uniform(-18, -12), gamma=parameter.Uniform(1, 7))
rn = gp_signals.FourierBasisGP(spectrum=pl, modes=f2[::2])
rnm = rn(self.psr)
# basis matrix test
msg = "F matrix incorrect for GP Fourier signal."
assert np.allclose(F, rnm.get_basis(params)), msg
# spectrum test
phi = utils.powerlaw(f2, log10_A=log10_A, gamma=gamma)
msg = "Spectrum incorrect for GP Fourier signal."
assert np.all(rnm.get_phi(params) == phi), msg
# inverse spectrum test
msg = "Spectrum inverse incorrect for GP Fourier signal."
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_fourier_red_noise(self):
"""Test that red noise signal returns correct values."""
# set up signal parameter
pl = utils.powerlaw(log10_A=parameter.Uniform(-18,-12),
gamma=parameter.Uniform(1,7))
rn = gs.FourierBasisGP(spectrum=pl, components=30)
rnm = rn(self.psr)
# parameters
log10_A, gamma = -14.5, 4.33
params = {'B1855+09_log10_A': log10_A,
'B1855+09_gamma': gamma}
# basis matrix test
F, f2 = utils.createfourierdesignmatrix_red(
self.psr.toas, nmodes=30)
msg = 'F matrix incorrect for GP Fourier signal.'
assert np.allclose(F, rnm.get_basis(params)), msg
# spectrum test
phi = utils.powerlaw(f2, log10_A=log10_A, gamma=gamma)
msg = 'Spectrum incorrect for GP Fourier signal.'
assert np.all(rnm.get_phi(params) == phi), msg
# inverse spectrum test
msg = 'Spectrum inverse incorrect for GP Fourier signal.'
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_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_red_noise_add(self):
"""Test that red noise addition only returns independent columns."""
# set up signals
pl = utils.powerlaw(log10_A=parameter.Uniform(-18,-12),
gamma=parameter.Uniform(1,7))
cpl = utils.powerlaw(log10_A=parameter.Uniform(-18,-12)('log10_Agw'),
gamma=parameter.Uniform(1,7)('gamma_gw'))
# parameters
log10_A, gamma = -14.5, 4.33
log10_Ac, gammac = -15.5, 1.33
params = {'B1855+09_log10_A': log10_A,
'B1855+09_gamma': gamma,
'log10_Agw': log10_Ac,
'gamma_gw': gammac}
Tmax = self.psr.toas.max() - self.psr.toas.min()
tpars = [(30, 20, Tmax, Tmax), (20, 30, Tmax, Tmax),
(30, 30, Tmax, Tmax), (30, 20, Tmax, 1.123*Tmax),
(20, 30, Tmax, 1.123*Tmax), (30, 30, 1.123*Tmax, Tmax)]
for (nf1, nf2, T1, T2) in tpars:
rn = gs.FourierBasisGP(spectrum=pl, components=nf1, Tspan=T1)
crn = gs.FourierBasisGP(spectrum=cpl, components=nf2, Tspan=T2)
s = rn + crn
rnm = s(self.psr)
# set up frequencies
F1, f1 = utils.createfourierdesignmatrix_red(
self.psr.toas, nmodes=nf1, Tspan=T1)
F2, f2 = utils.createfourierdesignmatrix_red(
self.psr.toas, nmodes=nf2, Tspan=T2)
# test power spectrum
p1 = utils.powerlaw(f1, log10_A, gamma)
p2 = utils.powerlaw(f2, log10_Ac, gammac)
if T1 == T2:
nf = max(2*nf1, 2*nf2)
phi = np.zeros(nf)
F = F1 if nf1 > nf2 else F2
phi[:2*nf1] = p1
phi[:2*nf2] += p2
F[:,]
else:
phi = np.concatenate((p1, p2))
F = np.hstack((F1, F2))
msg = 'Combined red noise PSD incorrect '
msg += 'for {} {} {} {}'.format(nf1, nf2, T1, T2)
assert np.all(rnm.get_phi(params) == phi), msg
msg = 'Combined red noise PSD inverse incorrect '
msg += 'for {} {} {} {}'.format(nf1, nf2, T1, T2)
assert np.all(rnm.get_phiinv(params) == 1/phi), msg
msg = 'Combined red noise Fmat incorrect '
msg += 'for {} {} {} {}'.format(nf1, nf2, T1, T2)
assert np.allclose(F, rnm.get_basis(params)), msg
def test_fourier_red_noise_backend(self):
"""Test that red noise-backend signal returns correct values."""
# set up signal parameter
pl = utils.powerlaw(log10_A=parameter.Uniform(-18, -12),
gamma=parameter.Uniform(1, 7))
selection = Selection(selections.by_backend)
rn = gp_signals.FourierBasisGP(spectrum=pl,
components=30,
selection=selection)
rnm = rn(self.psr)
# parameters
log10_As = [-14, -14.4, -15, -14.8]
gammas = [2.3, 4.4, 1.8, 5.6]
params = {
"B1855+09_red_noise_430_ASP_gamma": gammas[0],
"B1855+09_red_noise_430_PUPPI_gamma": gammas[1],
"B1855+09_red_noise_L-wide_ASP_gamma": gammas[2],
"B1855+09_red_noise_L-wide_PUPPI_gamma": gammas[3],
"B1855+09_red_noise_430_ASP_log10_A": log10_As[0],
"B1855+09_red_noise_430_PUPPI_log10_A": log10_As[1],
"B1855+09_red_noise_L-wide_ASP_log10_A": log10_As[2],
"B1855+09_red_noise_L-wide_PUPPI_log10_A": log10_As[3],
}
# get the basis
bflags = self.psr.backend_flags
Fmats, fs, phis = [], [], []
for ct, flag in enumerate(np.unique(bflags)):
mask = bflags == flag
F, f = utils.createfourierdesignmatrix_red(self.psr.toas[mask], 30)
Fmats.append(F)
fs.append(f)
phis.append(utils.powerlaw(f, log10_As[ct], gammas[ct]))
nf = sum(F.shape[1] for F in Fmats)
F = np.zeros((len(self.psr.toas), nf))
phi = np.hstack([p for p in phis])
nftot = 0
for ct, flag in enumerate(np.unique(bflags)):
mask = bflags == flag
nn = Fmats[ct].shape[1]
F[mask, nftot:nn + nftot] = Fmats[ct]
nftot += nn
msg = "F matrix incorrect for GP Fourier backend signal."
assert np.allclose(F, rnm.get_basis(params)), msg
# spectrum test
msg = "Spectrum incorrect for GP Fourier backend signal."
assert np.all(rnm.get_phi(params) == phi), msg
# inverse spectrum test
msg = "Spectrum inverse incorrect for GP Fourier backend signal."
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_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 = gs.BasisGP(pl, basis_env, name='env')
rn = gs.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_fourier_red_noise_backend(self):
"""Test that red noise-backend signal returns correct values."""
# set up signal parameter
pl = utils.powerlaw(log10_A=parameter.Uniform(-18,-12),
gamma=parameter.Uniform(1,7))
selection = Selection(selections.by_backend)
rn = gs.FourierBasisGP(spectrum=pl, components=30, selection=selection)
rnm = rn(self.psr)
# parameters
log10_As = [-14, -14.4, -15, -14.8]
gammas = [2.3, 4.4, 1.8, 5.6]
params = {'B1855+09_430_ASP_gamma': gammas[0],
'B1855+09_430_PUPPI_gamma': gammas[1],
'B1855+09_L-wide_ASP_gamma': gammas[2],
'B1855+09_L-wide_PUPPI_gamma': gammas[3],
'B1855+09_430_ASP_log10_A': log10_As[0],
'B1855+09_430_PUPPI_log10_A': log10_As[1],
'B1855+09_L-wide_ASP_log10_A': log10_As[2],
'B1855+09_L-wide_PUPPI_log10_A': log10_As[3]}
# get the basis
bflags = self.psr.backend_flags
Fmats, fs, phis = [], [], []
for ct, flag in enumerate(np.unique(bflags)):
mask = bflags == flag
F, f = utils.createfourierdesignmatrix_red(
self.psr.toas[mask], 30)
Fmats.append(F)
fs.append(f)
phis.append(utils.powerlaw(f, log10_As[ct], gammas[ct]))
nf = sum(F.shape[1] for F in Fmats)
F = np.zeros((len(self.psr.toas), nf))
phi = np.hstack(p for p in phis)
nftot = 0
for ct, flag in enumerate(np.unique(bflags)):
mask = bflags == flag
nn = Fmats[ct].shape[1]
F[mask, nftot:nn+nftot] = Fmats[ct]
nftot += nn
msg = 'F matrix incorrect for GP Fourier backend signal.'
assert np.allclose(F, rnm.get_basis(params)), msg
# spectrum test
msg = 'Spectrum incorrect for GP Fourier backend signal.'
assert np.all(rnm.get_phi(params) == phi), msg
# inverse spectrum test
msg = 'Spectrum inverse incorrect for GP Fourier backend signal.'
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 spin_noise(self, option="powerlaw"):
"""
Achromatic red noise process is called spin noise, although generally
this model is used to model any unknown red noise. If this model is
preferred over chromatic models then the observed noise is really spin
noise, associated with pulsar rotational irregularities.
"""
log10_A = parameter.Uniform(self.params.sn_lgA[0],
self.params.sn_lgA[1])
gamma = parameter.Uniform(self.params.sn_gamma[0],
self.params.sn_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)
sn = gp_signals.FourierBasisGP(spectrum=pl,
Tspan=self.params.Tspan,
name='red_noise',
components=nfreqs)
return sn
def paired_ppta_band_noise(self, option=[]):
"""
Including band noise terms for paired values of the PPTA "-B" flag:
joint 1020-cm and 4050-cm red processes.
"""
for ii, paired_band_term in enumerate(option):
log10_A = parameter.Uniform(self.params.syn_lgA[0],
self.params.syn_lgA[1])
gamma = parameter.Uniform(self.params.syn_gamma[0],\
self.params.syn_gamma[1])
pl = utils.powerlaw(log10_A=log10_A, gamma=gamma, \
components=self.params.red_general_nfouriercomp)
setattr(self, paired_band_term, globals()[paired_band_term])
nfreqs = self.determine_nfreqs(sel_func_name=paired_band_term)
pbn_term = gp_signals.FourierBasisGP(spectrum=pl, Tspan=self.params.Tspan,
name='band_noise_' + paired_band_term,
selection=selections.Selection( \
self.__dict__[paired_band_term] ),
components=nfreqs)
if ii == 0:
pbn = pbn_term
elif ii > 0:
pbn += pbn_term
return pbn
def red_noise_block(prior='log-uniform', Tspan=None):
"""
Returns red noise model:
1. Red noise modeled as a power-law with 30 sampling frequencies
: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.
"""
# red noise parameters
if prior == 'uniform':
log10_A = parameter.LinearExp(-20, -11)
elif prior == 'log-uniform':
log10_A = parameter.Uniform(-20, -11)
else:
raise ValueError('Unknown prior for red noise amplitude!')
gamma = parameter.Uniform(0, 7)
# red noise signal
pl = utils.powerlaw(log10_A=log10_A, gamma=gamma)
rn = gp_signals.FourierBasisGP(pl, components=30, Tspan=Tspan)
return rn
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 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_parameterized_orf(self):
T1 = 3.16e8
pl = utils.powerlaw(log10_A=parameter.Uniform(-18,-12),
gamma=parameter.Uniform(1,7))
orf = hd_orf_generic(a=parameter.Uniform(0,5),
b=parameter.Uniform(0,5),
c=parameter.Uniform(0,5))
rn = gp_signals.FourierBasisGP(spectrum=pl, Tspan=T1, components=30)
crn = gp_signals.FourierBasisCommonGP(spectrum=pl, orf=orf,
components=30, name='gw',
Tspan=T1)
model = rn + crn
pta = model(self.psrs[0]) + model(self.psrs[1])
lA1, gamma1 = -13, 1e-15
lA2, gamma2 = -13.3, 1e-15
lAc, gammac = -13.1, 1e-15
a, b, c = 1.9, 0.4, 0.23
params = {'gw_log10_A': lAc, 'gw_gamma': gammac,
'gw_a': a, 'gw_b':b, 'gw_c':c,
'B1855+09_log10_A': lA1, 'B1855+09_gamma': gamma1,
'J1909-3744_log10_A': lA2, 'J1909-3744_gamma': gamma2}
phi = pta.get_phi(params)
phiinv = pta.get_phiinv(params)
F1, f1 = utils.createfourierdesignmatrix_red(
self.psrs[0].toas, nmodes=30, Tspan=T1)
F2, f2 = utils.createfourierdesignmatrix_red(
self.psrs[1].toas, nmodes=30, Tspan=T1)
msg = 'F matrix incorrect'
assert np.allclose(pta.get_basis(params)[0], F1, rtol=1e-10), msg
assert np.allclose(pta.get_basis(params)[1], F2, rtol=1e-10), msg
nftot = 120
phidiag = np.zeros(nftot)
phit = np.zeros((nftot, nftot))
phidiag[:60] = utils.powerlaw(f1, lA1, gamma1)
phidiag[:60] += utils.powerlaw(f1, lAc, gammac)
phidiag[60:] = utils.powerlaw(f2, lA2, gamma2)
phidiag[60:] += utils.powerlaw(f2, lAc, gammac)
phit[np.diag_indices(nftot)] = phidiag
orf = hd_orf_generic(self.psrs[0].pos, self.psrs[1].pos, a=a, b=b, c=c)
spec = utils.powerlaw(f1, log10_A=lAc, gamma=gammac)
phit[:60, 60:] = np.diag(orf*spec)
phit[60:, :60] = phit[:60, 60:]
msg = '{} {}'.format(np.diag(phi), np.diag(phit))
assert np.allclose(phi, phit, rtol=1e-15, atol=1e-17), msg
msg = 'PTA Phi inverse is incorrect {}.'.format(params)
assert np.allclose(phiinv, np.linalg.inv(phit),
rtol=1e-15, atol=1e-17), msg
def gwb(self,option="hd_vary_gamma"):
"""
Spatially-correlated quadrupole signal from the nanohertz stochastic
gravitational-wave background.
"""
name = 'gw'
if "_nfreqs" in option:
split_idx_nfreqs = option.split('_').index('nfreqs') - 1
nfreqs = int(option.split('_')[split_idx_nfreqs])
else:
nfreqs = self.determine_nfreqs(sel_func_name=None, common_signal=True)
if "_gamma" in option:
amp_name = '{}_log10_A'.format(name)
if self.params.gwb_lgA_prior == "uniform":
gwb_log10_A = parameter.Uniform(self.params.gwb_lgA[0],
self.params.gwb_lgA[1])(amp_name)
elif self.params.gwb_lgA_prior == "linexp":
gwb_log10_A = parameter.LinearExp(self.params.gwb_lgA[0],
self.params.gwb_lgA[1])(amp_name)
gam_name = '{}_gamma'.format(name)
if "vary_gamma" in option:
gwb_gamma = parameter.Uniform(self.params.gwb_gamma[0],
self.params.gwb_gamma[1])(gam_name)
elif "fixed_gamma" in option:
gwb_gamma = parameter.Constant(4.33)(gam_name)
else:
split_idx_gamma = option.split('_').index('gamma') - 1
gamma_val = float(option.split('_')[split_idx_gamma])
gwb_gamma = parameter.Constant(gamma_val)(gam_name)
gwb_pl = utils.powerlaw(log10_A=gwb_log10_A, gamma=gwb_gamma)
elif "freesp" in option:
amp_name = '{}_log10_rho'.format(name)
log10_rho = parameter.Uniform(self.params.gwb_lgrho[0],
self.params.gwb_lgrho[1],
size=nfreqs)(amp_name)
gwb_pl = gp_priors.free_spectrum(log10_rho=log10_rho)
if "hd" in option:
orf = utils.hd_orf()
gwb = gp_signals.FourierBasisCommonGP(gwb_pl, orf, components=nfreqs,
name='gwb', Tspan=self.params.Tspan)
else:
gwb = gp_signals.FourierBasisGP(gwb_pl, components=nfreqs,
name='gwb', Tspan=self.params.Tspan)
return gwb
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 gwb(self,option="common_pl"):
"""
Spatially-correlated quadrupole signal from the nanohertz stochastic
gravitational-wave background.
"""
gwb_log10_A = parameter.Uniform(params.gwb_lgA[0],params.gwb_lgA[1])
if option=="common_pl":
gwb_gamma = parameter.Uniform(params.gwb_gamma[0],params.gwb_gamma[1])
elif option=="fixed_gamma":
gwb_gamma = parameter.Constant(4.33)
gwb_pl = utils.powerlaw(log10_A=gwb_log10_A, gamma=gwb_gamma)
nfreqs = self.determine_nfreqs(sel_func_name=None)
orf = utils.hd_orf()
gwb = gp_signals.FourierBasisCommonGP(gwb_pl, orf, components=nfreqs, \
name='gwb', Tspan=self.params.Tspan)
return gwb
def test_summary(self):
""" Test summary table."""
T1, T3 = 3.16e8, 3.16e8
nf1 = 30
pl = utils.powerlaw(log10_A=parameter.Uniform(-18,-12),
gamma=parameter.Uniform(1,7))
orf = utils.hd_orf()
rn = gp_signals.FourierBasisGP(spectrum=pl, components=nf1, Tspan=T1)
crn = gp_signals.FourierBasisCommonGP(spectrum=pl, orf=orf,
components=1, name='gw',
Tspan=T3)
model = rn + crn
pta = model(self.psrs[0]) + model(self.psrs[1])
pta.summary()
def ppta_band_noise(self,option=[]):
"""
Including red noise terms by the PPTA "-B" flag, only with flagvals in
noise model file. It is considered a derivative of system noise in our code.
See Lentati, Lindley, et al. MNRAS 458.2 (2016): 2161-2187.
"""
for ii, band_term in enumerate(option):
log10_A = parameter.Uniform(self.params.syn_lgA[0],self.params.syn_lgA[1])
gamma = parameter.Uniform(self.params.syn_gamma[0],\
self.params.syn_gamma[1])
selection_function_name = 'band_noise_selection_' + \
str(self.sys_noise_count)
setattr(self, selection_function_name,
selection_factory(selection_function_name))
band_term, nfreqs = self.option_nfreqs(band_term, \
selection_flag='B', \
sel_func_name=selection_function_name)
if "turnover" in band_term:
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 = band_term.split("_")
del option_split[option_split.index("turnover")]
band_term = "_".join(option_split)
else:
pl = utils.powerlaw(log10_A=log10_A, gamma=gamma, \
components=self.params.red_general_nfouriercomp)
tspan = self.determine_tspan(sel_func_name=selection_function_name)
syn_term = gp_signals.FourierBasisGP(spectrum=pl, Tspan=tspan,
name='band_noise_' + \
str(self.sys_noise_count),
selection=selections.Selection( \
self.__dict__[selection_function_name] ),
components=nfreqs)
if ii == 0:
syn = syn_term
elif ii > 0:
syn += syn_term
self.sys_noise_count += 1
return syn
def test_summary(self):
""" Test summary table."""
T1, T3 = 3.16e8, 3.16e8
nf1 = 30
pl = utils.powerlaw(log10_A=parameter.Uniform(-18, -12),
gamma=parameter.Uniform(1, 7))
orf = utils.hd_orf()
rn = gp_signals.FourierBasisGP(spectrum=pl, components=nf1, Tspan=T1)
crn = gp_signals.FourierBasisCommonGP(spectrum=pl,
orf=orf,
components=1,
name='gw',
Tspan=T3)
model = rn + crn
pta = model(self.psrs[0]) + model(self.psrs[1])
pta.summary(to_stdout=True)
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 test_psd(self):
"""Test PSD functions."""
Tmax = self.psr.toas.max() - self.psr.toas.min()
f = np.linspace(1 / Tmax, 10 / Tmax, 10)
log10_A = -15
gamma = 4.33
lf0 = -8.5
kappa = 10 / 3
beta = 0.5
pl = (10**log10_A)**2 / 12.0 / np.pi**2 * const.fyr**(gamma - 3) * f**(
-gamma) * f[0]
hcf = 10**log10_A * (f / const.fyr)**(
(3 - gamma) / 2) / (1 + (10**lf0 / f)**kappa)**beta
pt = hcf**2 / 12 / np.pi**2 / f**3 * f[0]
msg = "PSD calculation incorrect"
assert np.allclose(utils.powerlaw(f, log10_A, gamma), pl), msg
assert np.allclose(utils.turnover(f, log10_A, gamma, lf0, kappa, beta),
pt), msg
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_psd(self):
"""Test PSD functions."""
Tmax = self.psr.toas.max() - self.psr.toas.min()
f = np.linspace(1/Tmax, 10/Tmax, 10)
log10_A = -15
gamma = 4.33
lf0 = -8.5
kappa = 10/3
beta = 0.5
pl = ((10**log10_A)**2 / 12.0 / np.pi**2 *
const.fyr**(gamma-3) * f**(-gamma)*f[0])
hcf = (10**log10_A * (f / const.fyr) ** ((3-gamma) / 2) /
(1 + (10**lf0 / f) ** kappa) ** beta)
pt = hcf**2/12/np.pi**2/f**3 * f[0]
msg = 'PSD calculation incorrect'
assert np.allclose(utils.powerlaw(f, log10_A, gamma), pl), msg
assert np.allclose(utils.turnover(f, log10_A, gamma,
lf0, kappa, beta),pt), 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 paired_ppta_band_noise(self, option=[]):
"""
Including band noise terms for paired values of the PPTA "-B" flag:
joint 1020-cm and 4050-cm red processes.
"""
for ii, paired_band_term in enumerate(option):
log10_A = parameter.Uniform(self.params.syn_lgA[0],self.params.syn_lgA[1])
gamma = parameter.Uniform(self.params.syn_gamma[0],\
self.params.syn_gamma[1])
if "turnover" in paired_band_term:
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 = paired_band_term.split("_")
del option_split[option_split.index("turnover")]
paired_band_term = "_".join(option_split)
else:
pl = utils.powerlaw(log10_A=log10_A, gamma=gamma, \
components=self.params.red_general_nfouriercomp)
if "nfreqs" not in paired_band_term:
setattr(self, paired_band_term, globals()[paired_band_term])
paired_band_term, nfreqs = self.option_nfreqs(paired_band_term, \
sel_func_name=paired_band_term)
setattr(self, paired_band_term, globals()[paired_band_term])
tspan = self.determine_tspan(sel_func_name=paired_band_term)
pbn_term = gp_signals.FourierBasisGP(spectrum=pl, Tspan=tspan,
name='band_noise_' + paired_band_term,
selection=selections.Selection( \
self.__dict__[paired_band_term] ),
components=nfreqs)
if ii == 0:
pbn = pbn_term
elif ii > 0:
pbn += pbn_term
return pbn
def test_fourier_red_noise(self):
"""Test that implicit and explicit GP delays are the same."""
# set up signal parameter
pl = utils.powerlaw(log10_A=parameter.Uniform(-18, -12),
gamma=parameter.Uniform(1, 7))
rn = gp_signals.FourierBasisGP(spectrum=pl, components=20)
rnm = rn(self.psr)
rnc = gp_signals.FourierBasisGP(spectrum=pl,
components=20,
coefficients=True)
rnmc = rnc(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
}
# get the GP delays in two different ways
cf = np.random.randn(40)
d1 = np.dot(rnm.get_basis(params), cf)
params.update({"B1855+09_red_noise_coefficients": cf})
d2 = rnmc.get_delay(params)
msg = "Implicit and explicit GP delays are different."
assert np.allclose(d1, d2), msg
# np.array cast is needed because we get a KernelArray
phimat = np.array(rnm.get_phi(params))
pr1 = (-0.5 * np.sum(cf * cf / phimat) -
0.5 * np.sum(np.log(phimat)) -
0.5 * len(phimat) * np.log(2 * math.pi))
cpar = [p for p in rnmc.params if "coefficients" in p.name][0]
pr2 = cpar.get_logpdf(params=params)
msg = "Implicit and explicit GP priors are different."
assert np.allclose(pr1, pr2), msg
def ppta_band_noise(self, option=[]):
"""
Including red noise terms by the PPTA "-B" flag, only with flagvals in
noise model file. It is considered a derivative of system noise in our code.
See Lentati, Lindley, et al. MNRAS 458.2 (2016): 2161-2187.
"""
for ii, band_term in enumerate(option):
log10_A = parameter.Uniform(self.params.syn_lgA[0],
self.params.syn_lgA[1])
gamma = parameter.Uniform(self.params.syn_gamma[0],\
self.params.syn_gamma[1])
pl = utils.powerlaw(log10_A=log10_A, gamma=gamma, \
components=self.params.red_general_nfouriercomp)
selection_function_name = 'band_noise_selection_' + \
str(self.sys_noise_count)
setattr(self, selection_function_name,
selection_factory(selection_function_name))
self.psr.sys_flags.append('B')
self.psr.sys_flagvals.append(band_term)
nfreqs = self.determine_nfreqs(
sel_func_name=selection_function_name)
tspan = self.determine_tspan(sel_func_name=selection_function_name)
syn_term = gp_signals.FourierBasisGP(spectrum=pl, Tspan=tspan,
name='band_noise_' + \
str(self.sys_noise_count),
selection=selections.Selection( \
self.__dict__[selection_function_name] ),
components=nfreqs)
if ii == 0:
syn = syn_term
elif ii > 0:
syn += syn_term
self.sys_noise_count += 1
return syn
def system_noise(self,option=[]):
"""
Including red noise terms by "-group" flag, only with flagvals in noise
model file.
See Lentati, Lindley, et al. MNRAS 458.2 (2016): 2161-2187.
"""
for ii, sys_noise_term in enumerate(option):
log10_A = parameter.Uniform(self.params.syn_lgA[0],self.params.syn_lgA[1])
gamma = parameter.Uniform(self.params.syn_gamma[0],\
self.params.syn_gamma[1])
pl = utils.powerlaw(log10_A=log10_A, gamma=gamma, \
components=self.params.red_general_nfouriercomp)
selection_function_name = 'sys_noise_selection_'+str(self.sys_noise_count)
setattr(self, selection_function_name,
selection_factory(selection_function_name))
sys_noise_term, nfreqs = self.option_nfreqs(sys_noise_term, \
selection_flag='group', \
sel_func_name=selection_function_name)
tspan = self.determine_tspan(sel_func_name=selection_function_name)
syn_term = gp_signals.FourierBasisGP(spectrum=pl, Tspan=tspan,
name='system_noise_' + \
str(self.sys_noise_count),
selection=selections.Selection( \
self.__dict__[selection_function_name] ),
components=nfreqs)
if ii == 0:
syn = syn_term
elif ii > 0:
syn += syn_term
self.sys_noise_count += 1
return syn
def add_rn(self):
"""Return dictionary containing red noise power-law signal attributes
:return: OrderedDict of red noise signal
"""
log10_A = parameter.Uniform(-20.0, -10.0)
gamma = parameter.Uniform(0.02, 6.98)
pl = utils.powerlaw(log10_A=log10_A, gamma=gamma)
rn = gp_signals.FourierBasisGP(pl,
components=self.nfreqcomps,
name='rn')
newsignal = OrderedDict({
'type':
'rn',
'name': [self.pname + '_rn_log10_A', self.pname + '_rn_gamma'],
'pmin': [-20.0, 0.02],
'pmax': [-10.0, 6.98],
'pstart': [-14.5, 3.51],
'interval': [True, True],
'numpars':
2
})
self.rn_sig = rn(self.psr)
return {'rn': newsignal}
def test_pta_phiinv_methods(self):
ef = white_signals.MeasurementNoise(efac=parameter.Uniform(0.1, 5))
span = np.max(self.psrs[0].toas) - np.min(self.psrs[0].toas)
pl = utils.powerlaw(log10_A=parameter.Uniform(-16,-13),
gamma=parameter.Uniform(1,7))
orf = utils.hd_orf()
vrf = utils.dipole_orf()
rn = gp_signals.FourierBasisGP(spectrum=pl,
components=30, Tspan=span)
hdrn = gp_signals.FourierBasisCommonGP(spectrum=pl, orf=orf,
components=20, Tspan=span,
name='gw')
vrn = gp_signals.FourierBasisCommonGP(spectrum=pl, orf=vrf,
components=20, Tspan=span,
name='vec')
vrn2 = gp_signals.FourierBasisCommonGP(spectrum=pl, orf=vrf,
components=20, Tspan=span*1.234,
name='vec2')
# two common processes, sharing basis partially
model = ef + rn + hdrn # + vrn
pta = signal_base.PTA([model(psr) for psr in self.psrs])
ps = {p.name: float(p.sample()) for p in pta.params}
phi = pta.get_phi(ps)
ldp = np.linalg.slogdet(phi)[1]
inv1, ld1 = pta.get_phiinv(ps,method='cliques', logdet=True)
inv2, ld2 = pta.get_phiinv(ps,method='partition', logdet=True)
inv3, ld3 = pta.get_phiinv(ps,method='sparse', logdet=True)
inv3 = inv3.toarray()
for ld in [ld1, ld2, ld3]:
msg = "Wrong phi log determinant for two common processes"
assert np.allclose(ldp, ld, rtol=1e-15, atol=1e-6), msg
for inv in [inv1,inv2,inv3]:
msg = "Wrong phi inverse for two common processes"
assert np.allclose(np.dot(phi, inv), np.eye(phi.shape[0]),
rtol=1e-15, atol=1e-6), msg
for inva, invb in itertools.combinations([inv1,inv2,inv3],2):
assert np.allclose(inva,invb)
# two common processes, no sharing basis
model = ef + rn + vrn2
pta = signal_base.PTA([model(psr) for psr in self.psrs])
ps = {p.name: float(p.sample()) for p in pta.params}
phi = pta.get_phi(ps)
ldp = np.linalg.slogdet(phi)[1]
inv1, ld1 = pta.get_phiinv(ps,method='cliques', logdet=True)
inv2, ld2 = pta.get_phiinv(ps,method='partition', logdet=True)
inv3, ld3 = pta.get_phiinv(ps,method='sparse', logdet=True)
inv3 = inv3.toarray()
for ld in [ld1, ld2, ld3]:
msg = "Wrong phi log determinant for two common processes"
assert np.allclose(ldp, ld, rtol=1e-15, atol=1e-6), msg
for inv in [inv1,inv2,inv3]:
msg = "Wrong phi inverse for two processes"
assert np.allclose(np.dot(phi, inv), np.eye(phi.shape[0]),
rtol=1e-15, atol=1e-6), msg
for inva, invb in itertools.combinations([inv1,inv2,inv3],2):
assert np.allclose(inva,invb)
# three common processes, sharing basis partially
model = ef + rn + hdrn + vrn
pta = signal_base.PTA([model(psr) for psr in self.psrs])
ps = {p.name: float(p.sample()) for p in pta.params}
phi = pta.get_phi(ps)
ldp = np.linalg.slogdet(phi)[1]
inv1, ld1 = pta.get_phiinv(ps,method='cliques', logdet=True)
inv2, ld2 = pta.get_phiinv(ps,method='partition', logdet=True)
inv3, ld3 = pta.get_phiinv(ps,method='sparse', logdet=True)
inv3 = inv3.toarray()
for ld in [ld1, ld3]:
msg = "Wrong phi log determinant for two common processes"
assert np.allclose(ldp, ld, rtol=1e-15, atol=1e-6), msg
for inv in [inv1,inv3]:
msg = "Wrong phi inverse for three common processes"
assert np.allclose(np.dot(phi, inv), np.eye(phi.shape[0]),
rtol=1e-15, atol=1e-6), msg
for inva, invb in itertools.combinations([inv1,inv3],2):
assert np.allclose(inva,invb)
# four common processes, three sharing basis partially
model = ef + rn + hdrn + vrn + vrn2
pta = signal_base.PTA([model(psr) for psr in self.psrs])
ps = {p.name: float(p.sample()) for p in pta.params}
phi = pta.get_phi(ps)
ldp = np.linalg.slogdet(phi)[1]
inv1, ld1 = pta.get_phiinv(ps,method='cliques', logdet=True)
inv2, ld2 = pta.get_phiinv(ps,method='partition', logdet=True)
inv3, ld3 = pta.get_phiinv(ps,method='sparse', logdet=True)
inv3 = inv3.toarray()
for ld in [ld1, ld3]:
msg = "Wrong phi log determinant for two common processes"
assert np.allclose(ldp, ld, rtol=1e-15, atol=1e-6), msg
for inv in [inv1, inv3]:
msg = "Wrong phi inverse for four processes"
assert np.allclose(np.dot(phi, inv), np.eye(phi.shape[0]),
rtol=1e-15, atol=1e-6), msg
for inva, invb in itertools.combinations([inv1, inv3],2):
assert np.allclose(inva, invb)
def test_red_noise_add_backend(self):
"""Test that red noise with backend addition only returns
independent columns."""
# set up signals
pl = utils.powerlaw(log10_A=parameter.Uniform(-18, -12), gamma=parameter.Uniform(1, 7))
selection = Selection(selections.by_backend)
cpl = utils.powerlaw(
log10_A=parameter.Uniform(-18, -12)("log10_Agw"), gamma=parameter.Uniform(1, 7)("gamma_gw")
)
# parameters
log10_As = [-14, -14.4, -15, -14.8]
gammas = [2.3, 4.4, 1.8, 5.6]
log10_Ac, gammac = -15.5, 1.33
params = {
"B1855+09_red_noise_430_ASP_gamma": gammas[0],
"B1855+09_red_noise_430_PUPPI_gamma": gammas[1],
"B1855+09_red_noise_L-wide_ASP_gamma": gammas[2],
"B1855+09_red_noise_L-wide_PUPPI_gamma": gammas[3],
"B1855+09_red_noise_430_ASP_log10_A": log10_As[0],
"B1855+09_red_noise_430_PUPPI_log10_A": log10_As[1],
"B1855+09_red_noise_L-wide_ASP_log10_A": log10_As[2],
"B1855+09_red_noise_L-wide_PUPPI_log10_A": log10_As[3],
"log10_Agw": log10_Ac,
"gamma_gw": gammac,
}
Tmax = self.psr.toas.max() - self.psr.toas.min()
tpars = [
(30, 20, Tmax, Tmax),
(20, 30, Tmax, Tmax),
(30, 30, Tmax, Tmax),
(30, 20, Tmax, 1.123 * Tmax),
(20, 30, Tmax, 1.123 * Tmax),
(30, 30, 1.123 * Tmax, Tmax),
(30, 20, None, Tmax),
]
for (nf1, nf2, T1, T2) in tpars:
rn = gp_signals.FourierBasisGP(spectrum=pl, components=nf1, Tspan=T1, selection=selection)
crn = gp_signals.FourierBasisGP(spectrum=cpl, components=nf2, Tspan=T2)
s = rn + crn
rnm = s(self.psr)
# get the basis
bflags = self.psr.backend_flags
Fmats, fs, phis = [], [], []
F2, f2 = utils.createfourierdesignmatrix_red(self.psr.toas, nf2, Tspan=T2)
p2 = utils.powerlaw(f2, log10_Ac, gammac)
for ct, flag in enumerate(np.unique(bflags)):
mask = bflags == flag
F1, f1 = utils.createfourierdesignmatrix_red(self.psr.toas[mask], nf1, Tspan=T1)
Fmats.append(F1)
fs.append(f1)
phis.append(utils.powerlaw(f1, log10_As[ct], gammas[ct]))
Fmats.append(F2)
phis.append(p2)
nf = sum(F.shape[1] for F in Fmats)
F = np.zeros((len(self.psr.toas), nf))
phi = np.hstack([p for p in phis])
nftot = 0
for ct, flag in enumerate(np.unique(bflags)):
mask = bflags == flag
nn = Fmats[ct].shape[1]
F[mask, nftot : nn + nftot] = Fmats[ct]
nftot += nn
F[:, -2 * nf2 :] = F2
msg = "Combined red noise PSD incorrect "
msg += "for {} {} {} {}".format(nf1, nf2, T1, T2)
assert np.all(rnm.get_phi(params) == phi), msg
msg = "Combined red noise PSD inverse incorrect "
msg += "for {} {} {} {}".format(nf1, nf2, T1, T2)
assert np.all(rnm.get_phiinv(params) == 1 / phi), msg
msg = "Combined red noise Fmat incorrect "
msg += "for {} {} {} {}".format(nf1, nf2, T1, T2)
assert np.allclose(F, rnm.get_basis(params)), msg
def test_red_noise_add(self):
"""Test that red noise addition only returns independent columns."""
# set up signals
pl = utils.powerlaw(log10_A=parameter.Uniform(-18, -12), gamma=parameter.Uniform(1, 7))
cpl = utils.powerlaw(
log10_A=parameter.Uniform(-18, -12)("log10_Agw"), gamma=parameter.Uniform(1, 7)("gamma_gw")
)
# parameters
log10_A, gamma = -14.5, 4.33
log10_Ac, gammac = -15.5, 1.33
params = {
"B1855+09_red_noise_log10_A": log10_A,
"B1855+09_red_noise_gamma": gamma,
"log10_Agw": log10_Ac,
"gamma_gw": gammac,
}
Tmax = self.psr.toas.max() - self.psr.toas.min()
tpars = [
(30, 20, Tmax, Tmax),
(20, 30, Tmax, Tmax),
(30, 30, Tmax, Tmax),
(30, 20, Tmax, 1.123 * Tmax),
(20, 30, Tmax, 1.123 * Tmax),
(30, 30, 1.123 * Tmax, Tmax),
]
for (nf1, nf2, T1, T2) in tpars:
rn = gp_signals.FourierBasisGP(spectrum=pl, components=nf1, Tspan=T1)
crn = gp_signals.FourierBasisGP(spectrum=cpl, components=nf2, Tspan=T2)
s = rn + crn
rnm = s(self.psr)
# set up frequencies
F1, f1 = utils.createfourierdesignmatrix_red(self.psr.toas, nmodes=nf1, Tspan=T1)
F2, f2 = utils.createfourierdesignmatrix_red(self.psr.toas, nmodes=nf2, Tspan=T2)
# test power spectrum
p1 = utils.powerlaw(f1, log10_A, gamma)
p2 = utils.powerlaw(f2, log10_Ac, gammac)
if T1 == T2:
nf = max(2 * nf1, 2 * nf2)
phi = np.zeros(nf)
F = F1 if nf1 > nf2 else F2
phi[: 2 * nf1] = p1
phi[: 2 * nf2] += p2
F[
:,
] # noqa: E231
else:
phi = np.concatenate((p1, p2))
F = np.hstack((F1, F2))
msg = "Combined red noise PSD incorrect "
msg += "for {} {} {} {}".format(nf1, nf2, T1, T2)
assert np.all(rnm.get_phi(params) == phi), msg
msg = "Combined red noise PSD inverse incorrect "
msg += "for {} {} {} {}".format(nf1, nf2, T1, T2)
assert np.all(rnm.get_phiinv(params) == 1 / phi), msg
msg = "Combined red noise Fmat incorrect "
msg += "for {} {} {} {}".format(nf1, nf2, T1, T2)
assert np.allclose(F, rnm.get_basis(params)), msg
def test_pta_phi(self):
T1, T2, T3 = 3.16e8, 3.16e8, 3.16e8
nf1, nf2, nf3 = 2, 2, 1
pl = utils.powerlaw(log10_A=parameter.Uniform(-18,-12),
gamma=parameter.Uniform(1,7))
orf = utils.hd_orf()
rn = gp_signals.FourierBasisGP(spectrum=pl, components=nf1, Tspan=T1)
crn = gp_signals.FourierBasisCommonGP(spectrum=pl, orf=orf,
components=1, name='gw',
Tspan=T3)
model = rn + crn
pta = model(self.psrs[0]) + model(self.psrs[1])
lA1, gamma1 = -13, 1e-15
lA2, gamma2 = -13.3, 1e-15
lAc, gammac = -13.1, 1e-15
params = {'gw_log10_A': lAc, 'gw_gamma': gammac,
'B1855+09_log10_A': lA1, 'B1855+09_gamma': gamma1,
'J1909-3744_log10_A': lA2, 'J1909-3744_gamma': gamma2}
phi = pta.get_phi(params)
phiinv = pta.get_phiinv(params)
T1, T2, T3 = 3.16e8, 3.16e8, 3.16e8
nf1, nf2, nf3 = 2, 2, 1
F1, f1 = utils.createfourierdesignmatrix_red(
self.psrs[0].toas, nf1, Tspan=T1)
F2, f2 = utils.createfourierdesignmatrix_red(
self.psrs[1].toas, nf2, Tspan=T2)
F1c, fc = utils.createfourierdesignmatrix_red(
self.psrs[0].toas, nf3, Tspan=T3)
F2c, fc = utils.createfourierdesignmatrix_red(
self.psrs[1].toas, nf3, Tspan=T3)
nftot = 2 * 2 * nf1
phidiag = np.zeros(nftot)
phit = np.zeros((nftot, nftot))
phidiag[:4] = utils.powerlaw(f1, lA1, gamma1)
phidiag[:2] += utils.powerlaw(fc, lAc, gammac)
phidiag[4:] = utils.powerlaw(f2, lA2, gamma2)
phidiag[4:6] += utils.powerlaw(fc, lAc, gammac)
phit[np.diag_indices(nftot)] = phidiag
phit[:2, 4:6] = np.diag(hd_powerlaw(fc, self.psrs[0].pos,
self.psrs[1].pos, lAc,
gammac))
phit[4:6, :2] = np.diag(hd_powerlaw(fc, self.psrs[0].pos,
self.psrs[1].pos, lAc,
gammac))
msg = '{} {}'.format(np.diag(phi), np.diag(phit))
assert np.allclose(phi, phit, rtol=1e-15, atol=1e-17), msg
msg = 'PTA Phi inverse is incorrect {}.'.format(params)
assert np.allclose(phiinv, np.linalg.inv(phit),
rtol=1e-15, atol=1e-17), msg
def hd_powerlaw(f, pos1, pos2, log10_A=-15, gamma=4.3):
return utils.powerlaw(f, log10_A, gamma) * utils.hd_orf(pos1, pos2)
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,
Tspan=Tspan,
name='other_gw')
def test_red_noise_add_backend(self):
"""Test that red noise with backend addition only returns
independent columns."""
# set up signals
pl = utils.powerlaw(log10_A=parameter.Uniform(-18,-12),
gamma=parameter.Uniform(1,7))
selection = Selection(selections.by_backend)
cpl = utils.powerlaw(log10_A=parameter.Uniform(-18,-12)('log10_Agw'),
gamma=parameter.Uniform(1,7)('gamma_gw'))
# parameters
log10_As = [-14, -14.4, -15, -14.8]
gammas = [2.3, 4.4, 1.8, 5.6]
log10_Ac, gammac = -15.5, 1.33
params = {'B1855+09_430_ASP_gamma': gammas[0],
'B1855+09_430_PUPPI_gamma': gammas[1],
'B1855+09_L-wide_ASP_gamma': gammas[2],
'B1855+09_L-wide_PUPPI_gamma': gammas[3],
'B1855+09_430_ASP_log10_A': log10_As[0],
'B1855+09_430_PUPPI_log10_A': log10_As[1],
'B1855+09_L-wide_ASP_log10_A': log10_As[2],
'B1855+09_L-wide_PUPPI_log10_A': log10_As[3],
'log10_Agw': log10_Ac,
'gamma_gw': gammac}
Tmax = self.psr.toas.max() - self.psr.toas.min()
tpars = [(30, 20, Tmax, Tmax), (20, 30, Tmax, Tmax),
(30, 30, Tmax, Tmax), (30, 20, Tmax, 1.123*Tmax),
(20, 30, Tmax, 1.123*Tmax), (30, 30, 1.123*Tmax, Tmax),
(30, 20, None, Tmax)]
for (nf1, nf2, T1, T2) in tpars:
rn = gs.FourierBasisGP(spectrum=pl, components=nf1, Tspan=T1,
selection=selection)
crn = gs.FourierBasisGP(spectrum=cpl, components=nf2, Tspan=T2)
s = rn + crn
rnm = s(self.psr)
# get the basis
bflags = self.psr.backend_flags
Fmats, fs, phis = [], [], []
F2, f2 = utils.createfourierdesignmatrix_red(
self.psr.toas, nf2, Tspan=T2)
p2 = utils.powerlaw(f2, log10_Ac, gammac)
for ct, flag in enumerate(np.unique(bflags)):
mask = bflags == flag
F1, f1 = utils.createfourierdesignmatrix_red(
self.psr.toas[mask], nf1, Tspan=T1)
Fmats.append(F1)
fs.append(f1)
phis.append(utils.powerlaw(f1, log10_As[ct], gammas[ct]))
Fmats.append(F2)
phis.append(p2)
nf = sum(F.shape[1] for F in Fmats)
F = np.zeros((len(self.psr.toas), nf))
phi = np.hstack(p for p in phis)
nftot = 0
for ct, flag in enumerate(np.unique(bflags)):
mask = bflags == flag
nn = Fmats[ct].shape[1]
F[mask, nftot:nn+nftot] = Fmats[ct]
nftot += nn
F[:, -2*nf2:] = F2
msg = 'Combined red noise PSD incorrect '
msg += 'for {} {} {} {}'.format(nf1, nf2, T1, T2)
assert np.all(rnm.get_phi(params) == phi), msg
msg = 'Combined red noise PSD inverse incorrect '
msg += 'for {} {} {} {}'.format(nf1, nf2, T1, T2)
assert np.all(rnm.get_phiinv(params) == 1/phi), msg
msg = 'Combined red noise Fmat incorrect '
msg += 'for {} {} {} {}'.format(nf1, nf2, T1, T2)
assert np.allclose(F, rnm.get_basis(params)), msg
def test_combine_signals(self):
"""Test for combining different signals."""
# set up signal parameter
ecorr = parameter.Uniform(-10, -5)
ec = gs.EcorrBasisModel(log10_ecorr=ecorr)
pl = utils.powerlaw(log10_A=parameter.Uniform(-18,-12),
gamma=parameter.Uniform(1,7))
rn = gs.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 = gs.BasisGP(prior, basis, name='se')
ts = gs.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_log10_ecorr': ecorr,
'B1855+09_log10_A': log10_A,
'B1855+09_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
def common_red_noise_block(psd='powerlaw',
prior='log-uniform',
Tspan=None,
gamma_val=None,
orf=None,
name='gwb'):
"""
Returns common red noise model:
1. Red noise modeled with user defined PSD with
30 sampling frequencies. Available PSDs are
['powerlaw', 'turnover' 'spectrum']
:param psd:
PSD to use for common red noise signal. Available options
are ['powerlaw', 'turnover' 'spectrum']
: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 gamma_val:
Value of spectral index for power-law and turnover
models. By default spectral index is varied of 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 name: Name of common red process
"""
orfs = {
'hd': utils.hd_orf(),
'dipole': utils.dipole_orf(),
'monopole': utils.monopole_orf()
}
# common red noise parameters
if psd in ['powerlaw', 'turnover']:
amp_name = '{}_log10_A'.format(name)
if prior == 'uniform':
log10_Agw = parameter.LinearExp(-18, -11)(amp_name)
elif prior == 'log-uniform' and gamma_val is not None:
if np.abs(gamma_val - 4.33) < 0.1:
log10_Agw = parameter.Uniform(-18, -14)(amp_name)
else:
log10_Agw = parameter.Uniform(-18, -11)(amp_name)
else:
log10_Agw = parameter.Uniform(-18, -11)(amp_name)
gam_name = '{}_gamma'.format(name)
if gamma_val is not None:
gamma_gw = parameter.Constant(gamma_val)(gam_name)
else:
gamma_gw = parameter.Uniform(0, 7)(gam_name)
# common red noise PSD
if psd == 'powerlaw':
cpl = utils.powerlaw(log10_A=log10_Agw, gamma=gamma_gw)
elif psd == 'turnover':
kappa_name = '{}_kappa'.format(name)
lf0_name = '{}_log10_fbend'.format(name)
kappa_gw = parameter.Uniform(0, 7)(kappa_name)
lf0_gw = parameter.Uniform(-9, -7)(lf0_name)
cpl = utils.turnover(log10_A=log10_Agw,
gamma=gamma_gw,
lf0=lf0_gw,
kappa=kappa_gw)
if orf is None:
crn = gp_signals.FourierBasisGP(cpl, components=30, Tspan=Tspan)
elif orf in orfs.keys():
crn = gp_signals.FourierBasisCommonGP(cpl,
orfs[orf],
components=30,
Tspan=Tspan)
else:
raise ValueError('ORF {} not recognized'.format(orf))
return crn
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
for p, t in zip(parfiles, timfiles):
psr = Pulsar(p, t)
psrs.append(psr)
save1 = np.load('noisepars.npy')
save2 = np.load('noisepardict.npy')
save3 = np.load('dpdmpars-maxposprob.npy')
save4 = np.load('dpdmpardict.npy')
Dict = {save2[i]: save1[i] for i in range(len(save2))}
Dict.update({save4[i]: save3[i] for i in range(len(save4))})
# The Big Model
# dm noise
log10_A_dm = parameter.Constant()
gamma_dm = parameter.Constant()
pl_dm = utils.powerlaw(log10_A=log10_A_dm, gamma=gamma_dm)
dm_basis = utils.createfourierdesignmatrix_dm(nmodes=50, Tspan=None)
dmn = gp_signals.BasisGP(pl_dm, dm_basis, name='dm_gp', coefficients=False)
# spin noise
log10_A = parameter.Constant()
gamma = parameter.Constant()
pl = utils.powerlaw(log10_A=log10_A, gamma=gamma)
selection = selections.Selection(selections.no_selection)
spn = gp_signals.FourierBasisGP(pl,
components=50,
Tspan=None,
coefficients=False,
selection=selection,
modes=None)
dp = DPDM.dpdm_block(type_='Bayes')
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['{}_log10_A'.format(pname)])
gamma.append(params['{}_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