def test_orf(self):
"""Test ORF functions."""
p1 = np.array([0.3, -0.5, 0.7])
p2 = np.array([0.9, 0.1, -0.6])
# test auto terms
hd = utils.hd_orf(p1, p1)
hd_exp = 1.0
dp = utils.dipole_orf(p1, p1)
dp_exp = 1.0 + 1e-5
mp = utils.monopole_orf(p1, p1)
mp_exp = 1.0 + 1e-5
msg = 'ORF auto term incorrect for {}'
keys = ['hd', 'dipole', 'monopole']
vals = [(hd, hd_exp), (dp, dp_exp), (mp, mp_exp)]
for key, val in zip(keys, vals):
assert val[0] == val[1], msg.format(key)
# test off diagonal terms
hd = utils.hd_orf(p1, p2)
omc2 = (1 - np.dot(p1, p2)) / 2
hd_exp = 1.5 * omc2 * np.log(omc2) - 0.25 * omc2 + 0.5
dp = utils.dipole_orf(p1, p2)
dp_exp = np.dot(p1, p2)
mp = utils.monopole_orf(p1, p2)
mp_exp = 1.0
msg = 'ORF cross term incorrect for {}'
keys = ['hd', 'dipole', 'monopole']
vals = [(hd, hd_exp), (dp, dp_exp), (mp, mp_exp)]
for key, val in zip(keys, vals):
assert val[0] == val[1], msg.format(key)
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 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)
print('Number of Fourier frequencies for the GWB/CPL signal: ', nfreqs)
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:
print('Adding HD ORF')
orf = utils.hd_orf()
gwb = gp_signals.FourierBasisCommonGP(gwb_pl,
orf,
components=nfreqs,
name='gwb',
Tspan=self.params.Tspan)
elif "mono" in option:
print('Adding monopole ORF')
orf = utils.monopole_orf()
gwb = gp_signals.FourierBasisCommonGP(gwb_pl,
orf,
components=nfreqs,
name='gwb',
Tspan=self.params.Tspan)
elif "dipo" in option:
print('Adding dipole ORF')
orf = utils.dipole_orf()
gwb = gp_signals.FourierBasisCommonGP(gwb_pl,
orf,
components=nfreqs,
name='gwb',
Tspan=self.params.Tspan)
elif "varorf" in option:
corr_coeff = parameter.Uniform(-1., 1., size=7)('corr_coeff')
orf = infer_orf(corr_coeff=corr_coeff)
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_orf(self):
"""Test ORF functions."""
p1 = np.array([0.3, 0.648, 0.7])
p2 = np.array([0.2, 0.775, -0.6])
# test auto terms
#
hd = utils.hd_orf(p1, p1)
hd_exp = 1.0
#
dp = utils.dipole_orf(p1, p1)
dp_exp = 1.0 + 1e-5
#
mp = utils.monopole_orf(p1, p1)
mp_exp = 1.0 + 1e-5
#
psr_positions = np.array([[1.318116071652818, 2.2142974355881808],
[1.1372584174390601, 0.79539883018414359]])
anis_basis = anis.anis_basis(psr_positions, lmax=1)
anis_orf = round(
utils.anis_orf(p1,
p1, [0.0, 1.0, 0.0],
anis_basis=anis_basis,
psrs_pos=[p1, p2],
lmax=1), 3)
anis_orf_exp = 1.147
#
msg = "ORF auto term incorrect for {}"
keys = ["hd", "dipole", "monopole", "anisotropy"]
vals = [(hd, hd_exp), (dp, dp_exp), (mp, mp_exp),
(anis_orf, anis_orf_exp)]
for key, val in zip(keys, vals):
assert val[0] == val[1], msg.format(key)
# test off diagonal terms
#
hd = utils.hd_orf(p1, p2)
omc2 = (1 - np.dot(p1, p2)) / 2
hd_exp = 1.5 * omc2 * np.log(omc2) - 0.25 * omc2 + 0.5
#
dp = utils.dipole_orf(p1, p2)
dp_exp = np.dot(p1, p2)
#
mp = utils.monopole_orf(p1, p2)
mp_exp = 1.0
#
psr_positions = np.array([[1.318116071652818, 2.2142974355881808],
[1.1372584174390601, 0.79539883018414359]])
anis_basis = anis.anis_basis(psr_positions, lmax=1)
anis_orf = round(
utils.anis_orf(p1,
p2, [0.0, 1.0, 0.0],
anis_basis=anis_basis,
psrs_pos=[p1, p2],
lmax=1), 3)
anis_orf_exp = -0.150
#
msg = "ORF cross term incorrect for {}"
keys = ["hd", "dipole", "monopole", "anisotropy"]
vals = [(hd, hd_exp), (dp, dp_exp), (mp, mp_exp),
(anis_orf, anis_orf_exp)]
for key, val in zip(keys, vals):
assert val[0] == val[1], msg.format(key)
def common_red_noise_block(psd='powerlaw',
prior='log-uniform',
Tspan=None,
components=30,
log10_A_val=None,
gamma_val=None,
delta_val=None,
orf=None,
orf_ifreq=0,
leg_lmax=5,
name='gw',
coefficients=False,
pshift=False,
pseed=None):
"""
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', 'broken_powerlaw']
: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 individual pulsar.
:param log10_A_val:
Value of log10_A parameter for fixed amplitude analyses.
:param gamma_val:
Value of spectral index for power-law and turnover
models. By default spectral index is varied of range [0,7]
:param delta_val:
Value of spectral index for high frequencies in broken power-law
and turnover models. By default spectral index is varied in 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 orf_ifreq:
Frequency bin at which to start the Hellings & Downs function with
numbering beginning at 0. Currently only works with freq_hd orf.
:param leg_lmax:
Maximum multipole of a Legendre polynomial series representation
of the overlap reduction function [default=5]
:param pshift:
Option to use a random phase shift in design matrix. For testing the
null hypothesis.
:param pseed:
Option to provide a seed for the random phase shift.
:param name: Name of common red process
"""
orfs = {
'crn':
None,
'hd':
utils.hd_orf(),
'dipole':
utils.dipole_orf(),
'monopole':
utils.monopole_orf(),
'param_hd':
model_orfs.param_hd_orf(a=parameter.Uniform(-1.5,
3.0)('gw_orf_param0'),
b=parameter.Uniform(-1.0,
0.5)('gw_orf_param1'),
c=parameter.Uniform(-1.0,
1.0)('gw_orf_param2')),
'spline_orf':
model_orfs.spline_orf(
params=parameter.Uniform(-0.9, 0.9, size=7)('gw_orf_spline')),
'bin_orf':
model_orfs.bin_orf(
params=parameter.Uniform(-1.0, 1.0, size=7)('gw_orf_bin')),
'zero_diag_hd':
model_orfs.zero_diag_hd(),
'zero_diag_bin_orf':
model_orfs.zero_diag_bin_orf(params=parameter.Uniform(
-1.0, 1.0, size=7)('gw_orf_bin_zero_diag')),
'freq_hd':
model_orfs.freq_hd(params=[components, orf_ifreq]),
'legendre_orf':
model_orfs.legendre_orf(
params=parameter.Uniform(-1.0, 1.0, size=leg_lmax +
1)('gw_orf_legendre')),
'zero_diag_legendre_orf':
model_orfs.zero_diag_legendre_orf(
params=parameter.Uniform(-1.0, 1.0, size=leg_lmax +
1)('gw_orf_legendre_zero_diag'))
}
# common red noise parameters
if psd in ['powerlaw', 'turnover', 'turnover_knee', 'broken_powerlaw']:
amp_name = '{}_log10_A'.format(name)
if log10_A_val is not None:
log10_Agw = parameter.Constant(log10_A_val)(amp_name)
else:
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 == 'broken_powerlaw':
delta_name = '{}_delta'.format(name)
kappa_name = '{}_kappa'.format(name)
log10_fb_name = '{}_log10_fb'.format(name)
kappa_gw = parameter.Uniform(0.01, 0.5)(kappa_name)
log10_fb_gw = parameter.Uniform(-10, -7)(log10_fb_name)
if delta_val is not None:
delta_gw = parameter.Constant(delta_val)(delta_name)
else:
delta_gw = parameter.Uniform(0, 7)(delta_name)
cpl = gpp.broken_powerlaw(log10_A=log10_Agw,
gamma=gamma_gw,
delta=delta_gw,
log10_fb=log10_fb_gw,
kappa=kappa_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)
elif psd == 'turnover_knee':
kappa_name = '{}_kappa'.format(name)
lfb_name = '{}_log10_fbend'.format(name)
delta_name = '{}_delta'.format(name)
lfk_name = '{}_log10_fknee'.format(name)
kappa_gw = parameter.Uniform(0, 7)(kappa_name)
lfb_gw = parameter.Uniform(-9.3, -8)(lfb_name)
delta_gw = parameter.Uniform(-2, 0)(delta_name)
lfk_gw = parameter.Uniform(-8, -7)(lfk_name)
cpl = gpp.turnover_knee(log10_A=log10_Agw,
gamma=gamma_gw,
lfb=lfb_gw,
lfk=lfk_gw,
kappa=kappa_gw,
delta=delta_gw)
if psd == 'spectrum':
rho_name = '{}_log10_rho'.format(name)
if prior == 'uniform':
log10_rho_gw = parameter.LinearExp(-9, -4,
size=components)(rho_name)
elif prior == 'log-uniform':
log10_rho_gw = parameter.Uniform(-9, -4, size=components)(rho_name)
cpl = gpp.free_spectrum(log10_rho=log10_rho_gw)
if orf is None:
crn = gp_signals.FourierBasisGP(cpl,
coefficients=coefficients,
components=components,
Tspan=Tspan,
name=name,
pshift=pshift,
pseed=pseed)
elif orf in orfs.keys():
if orf == 'crn':
crn = gp_signals.FourierBasisGP(cpl,
coefficients=coefficients,
components=components,
Tspan=Tspan,
name=name,
pshift=pshift,
pseed=pseed)
else:
crn = gp_signals.FourierBasisCommonGP(cpl,
orfs[orf],
components=components,
Tspan=Tspan,
name=name,
pshift=pshift,
pseed=pseed)
elif isinstance(orf, types.FunctionType):
crn = gp_signals.FourierBasisCommonGP(cpl,
orf,
components=components,
Tspan=Tspan,
name=name,
pshift=pshift,
pseed=pseed)
else:
raise ValueError('ORF {} not recognized'.format(orf))
return crn
def gwb(self,option="hd_vary_gamma"):
"""
Spatially-correlated quadrupole signal from the nanohertz stochastic
gravitational-wave background.
"""
name = 'gw'
optsp = option.split('+')
for option in optsp:
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)
print('Number of Fourier frequencies for the GWB/CPL signal: ', nfreqs)
if "_gamma" in option:
amp_name = '{}_log10_A'.format(name)
if (len(optsp) > 1 and 'hd' in option) or ('namehd' in option):
amp_name += '_hd'
elif (len(optsp) > 1 and ('varorf' in option or \
'interporf' in option)) \
or ('nameorf' in option):
amp_name += '_orf'
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:
print('Adding HD ORF')
if "noauto" in option:
print('Removing auto-correlation')
orf = hd_orf_noauto()
else:
orf = utils.hd_orf()
if len(optsp) > 1 or 'namehd' in option:
gwname = 'gw_hd'
else:
gwname = 'gw'
gwb = gp_signals.FourierBasisCommonGP(gwb_pl, orf, components=nfreqs,
name=gwname,
Tspan=self.params.Tspan)
elif "mono" in option:
print('Adding monopole ORF')
orf = utils.monopole_orf()
gwb = gp_signals.FourierBasisCommonGP(gwb_pl, orf, components=nfreqs,
name='gw',
Tspan=self.params.Tspan)
elif "dipo" in option:
print('Adding dipole ORF')
orf = utils.dipole_orf()
gwb = gp_signals.FourierBasisCommonGP(gwb_pl, orf, components=nfreqs,
name='gw',
Tspan=self.params.Tspan)
else:
gwb = gp_signals.FourierBasisGP(gwb_pl, components=nfreqs,
name='gw', Tspan=self.params.Tspan)
if 'gw_total' in locals():
gwb_total += gwb
else:
gwb_total = gwb
return gwb_total
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 = parameter.sample(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)
if not isinstance(inv3, np.ndarray):
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 = parameter.sample(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)
if not isinstance(inv3, np.ndarray):
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 = parameter.sample(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)
if not isinstance(inv3, np.ndarray):
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 = parameter.sample(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)
if not isinstance(inv3, np.ndarray):
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 common_red_noise_block(psd='powerlaw',
prior='log-uniform',
Tspan=None,
components=30,
gamma_val=None,
orf=None,
name='gw',
coefficients=False,
pshift=False,
pseed=None):
"""
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 pshift:
Option to use a random phase shift in design matrix. For testing the
null hypothesis.
:param pseed:
Option to provide a seed for the random phase shift.
: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', 'turnover_knee']:
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)
elif psd == 'turnover_knee':
kappa_name = '{}_kappa'.format(name)
lfb_name = '{}_log10_fbend'.format(name)
delta_name = '{}_delta'.format(name)
lfk_name = '{}_log10_fknee'.format(name)
kappa_gw = parameter.Uniform(0, 7)(kappa_name)
lfb_gw = parameter.Uniform(-9.3, -8)(lfb_name)
delta_gw = parameter.Uniform(-2, 0)(delta_name)
lfk_gw = parameter.Uniform(-8, -7)(lfk_name)
cpl = gpp.turnover_knee(log10_A=log10_Agw,
gamma=gamma_gw,
lfb=lfb_gw,
lfk=lfk_gw,
kappa=kappa_gw,
delta=delta_gw)
if psd == 'spectrum':
rho_name = '{}_log10_rho'.format(name)
if prior == 'uniform':
log10_rho_gw = parameter.LinearExp(-9, -4,
size=components)(rho_name)
elif prior == 'log-uniform':
log10_rho_gw = parameter.Uniform(-9, -4, size=components)(rho_name)
cpl = gpp.free_spectrum(log10_rho=log10_rho_gw)
if orf is None:
crn = gp_signals.FourierBasisGP(cpl,
coefficients=coefficients,
components=components,
Tspan=Tspan,
name=name,
pshift=pshift,
pseed=pseed)
elif orf in orfs.keys():
crn = gp_signals.FourierBasisCommonGP(cpl,
orfs[orf],
components=components,
Tspan=Tspan,
name=name,
pshift=pshift,
pseed=pseed)
elif isinstance(orf, types.FunctionType):
crn = gp_signals.FourierBasisCommonGP(cpl,
orf,
components=components,
Tspan=Tspan,
name=name,
pshift=pshift,
pseed=pseed)
else:
raise ValueError('ORF {} not recognized'.format(orf))
return crn
def gwb(self,option="hd_vary_gamma"):
"""
Spatially-correlated quadrupole signal from the nanohertz stochastic
gravitational-wave background.
"""
name = 'gw'
optsp = option.split('+')
for option in optsp:
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)
print('Number of Fourier frequencies for the GWB/CPL signal: ', nfreqs)
if "_gamma" in option:
amp_name = '{}_log10_A'.format(name)
if (len(optsp) > 1 and 'hd' in option) or ('namehd' in option):
amp_name += '_hd'
elif (len(optsp) > 1 and ('varorf' in option or \
'interporf' in option)) \
or ('nameorf' in option):
amp_name += '_orf'
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)
elif self.params.gwb_lgA_prior == "normal":
gwb_log10_A = parameter.Normal(mu=self.params.gwb_lgA[0],
sigma=self.params.gwb_lgA[1])(amp_name)
gam_name = '{}_gamma'.format(name)
if "vary_gamma" in option:
if self.params.gwb_gamma_prior == "uniform":
gwb_gamma = parameter.Uniform(self.params.gwb_gamma[0],
self.params.gwb_gamma[1])(gam_name)
if self.params.gwb_gamma_prior == "normal":
gwb_gamma = parameter.Normal(sigma=self.params.gwb_gamma[1],
mu=self.params.gwb_gamma[0])(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:
print('Adding HD ORF')
if "noauto" in option:
print('Removing auto-correlation')
orf = hd_orf_noauto()
else:
import time
print('AZ about to do hd orf', time.perf_counter())
orf = utils.hd_orf()
print('AZ called utils.hd_orf', time.perf_counter())
if len(optsp) > 1 or 'namehd' in option:
gwname = 'gwb_hd'
else:
gwname = 'gwb'
#print('evaluating gwb fourierbasiscommongp', time.perf_counter())
gwb = gp_signals.FourierBasisCommonGP(gwb_pl, orf, components=nfreqs,
name=gwname,
Tspan=self.params.Tspan)
#print('evaluating gwb fourierbasiscommongp', time.perf_counter())
elif "mono" in option:
print('Adding monopole ORF')
orf = utils.monopole_orf()
gwb = gp_signals.FourierBasisCommonGP(gwb_pl, orf, components=nfreqs,
name='gwb',
Tspan=self.params.Tspan)
elif "dipo" in option:
print('Adding dipole ORF')
orf = utils.dipole_orf()
gwb = gp_signals.FourierBasisCommonGP(gwb_pl, orf, components=nfreqs,
name='gwb',
Tspan=self.params.Tspan)
elif "halfdip" in option:
print('Adding dipole/2 ORF')
orf = halfdip_orf()
gwb = gp_signals.FourierBasisCommonGP(gwb_pl, orf, components=nfreqs,
name='gwb',
Tspan=self.params.Tspan)
elif "varorf" in option:
if len(optsp) > 1 or 'nameorf' in option:
gwname = 'gwb_orf'
else:
gwname = 'gwb'
corr_coeff = parameter.Uniform(-1., 1., size=7)('corr_coeff')
if "noauto" in option:
orf = infer_orf_noauto(corr_coeff=corr_coeff)
else:
orf = infer_orf(corr_coeff=corr_coeff)
gwb = gp_signals.FourierBasisCommonGP(gwb_pl, orf, components=nfreqs,
name=gwname,
Tspan=self.params.Tspan)
elif "interporf" in option:
print("Adding numpy-interpolated free ORF")
if len(optsp) > 1 or 'nameorf' in option:
gwname = 'gwb_orf'
else:
gwname = 'gwb'
corr_coeff = parameter.Uniform(-1., 1., size=7)('corr_coeff')
if "noauto" in option:
orf = infer_orf_npinterp_noauto(corr_coeff=corr_coeff)
else:
orf = infer_orf_npinterp(corr_coeff=corr_coeff)
if "skyscr" in option:
gwb = FourierBasisSkyscrambledGP(gwb_pl, orf, components=nfreqs,
name=gwname+'_skyscr',
Tspan=self.params.Tspan)
else:
gwb = gp_signals.FourierBasisCommonGP(gwb_pl, orf, components=nfreqs,
name=gwname,
Tspan=self.params.Tspan)
else:
gwb = gp_signals.FourierBasisGP(gwb_pl, components=nfreqs,
name='gwb', Tspan=self.params.Tspan)
if 'gwb_total' in locals():
gwb_total += gwb
else:
gwb_total = gwb
return gwb_total
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)