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 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 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 dm_noise_block(gp_kernel='diag',
psd='powerlaw',
nondiag_kernel='periodic',
prior='log-uniform',
Tspan=None,
components=30,
gamma_val=None):
"""
Returns DM noise model:
1. DM noise modeled as a power-law with 30 sampling frequencies
:param psd:
PSD function [e.g. powerlaw (default), turnover, free spectrum]
:param prior:
Prior on log10_A. Default if "log-uniform". Use "uniform" for
upper limits.
:param Tspan:
Sets frequency sampling f_i = i / Tspan. Default will
use overall time span for indivicual pulsar.
:param components:
Number of frequencies in sampling of DM-variations.
:param gamma_val:
If given, this is the fixed slope of the power-law for
powerlaw or turnover DM-variations
"""
# dm noise parameters that are common
if gp_kernel == 'diag':
if psd in ['powerlaw', 'turnover']:
# parameters shared by PSD functions
if prior == 'uniform':
log10_A_dm = parameter.LinearExp(-20, -11)
elif prior == 'log-uniform' and gamma_val is not None:
if np.abs(gamma_val - 4.33) < 0.1:
log10_A_dm = parameter.Uniform(-20, -11)
else:
log10_A_dm = parameter.Uniform(-20, -11)
else:
log10_A_dm = parameter.Uniform(-20, -11)
if gamma_val is not None:
gamma_dm = parameter.Constant(gamma_val)
else:
gamma_dm = parameter.Uniform(0, 7)
# different PSD function parameters
if psd == 'powerlaw':
dm_prior = utils.powerlaw(log10_A=log10_A_dm, gamma=gamma_dm)
elif psd == 'turnover':
kappa_dm = parameter.Uniform(0, 7)
lf0_dm = parameter.Uniform(-9, -7)
dm_prior = utils.turnover(log10_A=log10_A_dm,
gamma=gamma_dm,
lf0=lf0_dm,
kappa=kappa_dm)
if psd == 'spectrum':
if prior == 'uniform':
log10_rho_dm = parameter.LinearExp(-10, -4, size=components)
elif prior == 'log-uniform':
log10_rho_dm = parameter.Uniform(-10, -4, size=components)
dm_prior = free_spectrum(log10_rho=log10_rho_dm)
dm_basis = utils.createfourierdesignmatrix_dm(nmodes=components,
Tspan=Tspan)
elif gp_kernel == 'nondiag':
if nondiag_kernel == 'periodic':
# Periodic GP kernel for DM
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
period = parameter.Uniform(0.2, 5.0)
gam_p = parameter.Uniform(0.1, 30.0)
dm_basis = linear_interp_basis_dm(dt=15 * const.day)
dm_prior = periodic_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell,
gam_p=gam_p,
p=period)
elif nondiag_kernel == 'periodic_rfband':
# Periodic GP kernel for DM with RQ radio-frequency dependence
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
log10_ell2 = parameter.Uniform(2, 7)
alpha_wgt = parameter.Uniform(0.2, 6)
period = parameter.Uniform(0.2, 5.0)
gam_p = parameter.Uniform(0.1, 30.0)
dm_basis = get_tf_quantization_matrix(df=200,
dt=15 * const.day,
dm=True)
dm_prior = tf_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell,
gam_p=gam_p,
p=period,
alpha_wgt=alpha_wgt,
log10_ell2=log10_ell2)
elif nondiag_kernel == 'dmx_like':
# DMX-like signal
log10_sigma = parameter.Uniform(-10, -4)
dm_basis = linear_interp_basis_dm(dt=30 * const.day)
dm_prior = dmx_ridge_prior(log10_sigma=log10_sigma)
dmgp = gp_signals.BasisGP(dm_prior, dm_basis, name='dm_gp')
return dmgp
def 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 chromatic_noise_block(gp_kernel='nondiag',
psd='powerlaw',
nondiag_kernel='periodic',
prior='log-uniform',
dt=15,
df=200,
idx=4,
include_quadratic=False,
Tspan=None,
name='chrom',
components=30,
coefficients=False):
"""
Returns GP chromatic noise model :
1. Chromatic modeled with user defined PSD with
30 sampling frequencies. Available PSDs are
['powerlaw', 'turnover' 'spectrum']
:param gp_kernel:
Whether to use a diagonal kernel for the GP. ['diag','nondiag']
:param nondiag_kernel:
Which nondiagonal kernel to use for the GP.
['periodic','sq_exp','periodic_rfband','sq_exp_rfband']
:param psd:
PSD to use for common red noise signal. Available options
are ['powerlaw', 'turnover' 'spectrum']
:param prior:
What type of prior to use for amplitudes. ['log-uniform','uniform']
:param dt:
time-scale for linear interpolation basis (days)
:param df:
frequency-scale for linear interpolation basis (MHz)
:param idx:
Index of radio frequency dependence (i.e. DM is 2). Any float will work.
:param include_quadratic:
Whether to include a quadratic fit.
:param name: Name of signal
:param Tspan:
Tspan from which to calculate frequencies for PSD-based GPs.
:param components:
Number of frequencies to use in 'diag' GPs.
:param coefficients:
Whether to keep coefficients of the GP.
"""
if gp_kernel == 'diag':
chm_basis = gpb.createfourierdesignmatrix_chromatic(nmodes=components,
Tspan=Tspan)
if psd in ['powerlaw', 'turnover']:
if prior == 'uniform':
log10_A = parameter.LinearExp(-18, -11)
elif prior == 'log-uniform':
log10_A = parameter.Uniform(-18, -11)
gamma = parameter.Uniform(0, 7)
# PSD
if psd == 'powerlaw':
chm_prior = utils.powerlaw(log10_A=log10_A, gamma=gamma)
elif psd == 'turnover':
kappa = parameter.Uniform(0, 7)
lf0 = parameter.Uniform(-9, -7)
chm_prior = utils.turnover(log10_A=log10_A,
gamma=gamma,
lf0=lf0,
kappa=kappa)
if psd == 'spectrum':
if prior == 'uniform':
log10_rho = parameter.LinearExp(-10, -4, size=components)
elif prior == 'log-uniform':
log10_rho = parameter.Uniform(-10, -4, size=components)
chm_prior = gpp.free_spectrum(log10_rho=log10_rho)
elif gp_kernel == 'nondiag':
if nondiag_kernel == 'periodic':
# Periodic GP kernel for DM
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
log10_p = parameter.Uniform(-4, 1)
log10_gam_p = parameter.Uniform(-3, 2)
chm_basis = gpk.linear_interp_basis_chromatic(dt=dt * const.day)
chm_prior = gpk.periodic_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell,
log10_gam_p=log10_gam_p,
log10_p=log10_p)
elif nondiag_kernel == 'periodic_rfband':
# Periodic GP kernel for DM with RQ radio-frequency dependence
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
log10_ell2 = parameter.Uniform(2, 7)
log10_alpha_wgt = parameter.Uniform(-4, 1)
log10_p = parameter.Uniform(-4, 1)
log10_gam_p = parameter.Uniform(-3, 2)
chm_basis = gpk.get_tf_quantization_matrix(df=df,
dt=dt * const.day,
dm=True,
idx=idx)
chm_prior = gpk.tf_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell,
log10_gam_p=log10_gam_p,
log10_p=log10_p,
log10_alpha_wgt=log10_alpha_wgt,
log10_ell2=log10_ell2)
elif nondiag_kernel == 'sq_exp':
# squared-exponential kernel for DM
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
chm_basis = gpk.linear_interp_basis_chromatic(dt=dt * const.day,
idx=idx)
chm_prior = gpk.se_dm_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell)
elif nondiag_kernel == 'sq_exp_rfband':
# Sq-Exp GP kernel for Chrom with RQ radio-frequency dependence
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
log10_ell2 = parameter.Uniform(2, 7)
log10_alpha_wgt = parameter.Uniform(-4, 1)
dm_basis = gpk.get_tf_quantization_matrix(df=df,
dt=dt * const.day,
dm=True,
idx=idx)
dm_prior = gpk.sf_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell,
log10_alpha_wgt=log10_alpha_wgt,
log10_ell2=log10_ell2)
cgp = gp_signals.BasisGP(chm_prior,
chm_basis,
name=name + '_gp',
coefficients=coefficients)
if include_quadratic:
# quadratic piece
basis_quad = chrom.chromatic_quad_basis(idx=idx)
prior_quad = chrom.chromatic_quad_prior()
cquad = gp_signals.BasisGP(prior_quad, basis_quad, name=name + '_quad')
cgp += cquad
return cgp
def dm_noise_block(gp_kernel='diag',
psd='powerlaw',
nondiag_kernel='periodic',
prior='log-uniform',
dt=15,
df=200,
Tspan=None,
components=30,
gamma_val=None,
coefficients=False):
"""
Returns DM noise model:
1. DM noise modeled as a power-law with 30 sampling frequencies
:param psd:
PSD function [e.g. powerlaw (default), spectrum, tprocess]
:param prior:
Prior on log10_A. Default if "log-uniform". Use "uniform" for
upper limits.
:param dt:
time-scale for linear interpolation basis (days)
:param df:
frequency-scale for linear interpolation basis (MHz)
:param Tspan:
Sets frequency sampling f_i = i / Tspan. Default will
use overall time span for indivicual pulsar.
:param components:
Number of frequencies in sampling of DM-variations.
:param gamma_val:
If given, this is the fixed slope of the power-law for
powerlaw, turnover, or tprocess DM-variations
"""
# dm noise parameters that are common
if gp_kernel == 'diag':
if psd in ['powerlaw', 'turnover', 'tprocess', 'tprocess_adapt']:
# parameters shared by PSD functions
if prior == 'uniform':
log10_A_dm = parameter.LinearExp(-20, -11)
elif prior == 'log-uniform' and gamma_val is not None:
if np.abs(gamma_val - 4.33) < 0.1:
log10_A_dm = parameter.Uniform(-20, -11)
else:
log10_A_dm = parameter.Uniform(-20, -11)
else:
log10_A_dm = parameter.Uniform(-20, -11)
if gamma_val is not None:
gamma_dm = parameter.Constant(gamma_val)
else:
gamma_dm = parameter.Uniform(0, 7)
# different PSD function parameters
if psd == 'powerlaw':
dm_prior = utils.powerlaw(log10_A=log10_A_dm, gamma=gamma_dm)
elif psd == 'turnover':
kappa_dm = parameter.Uniform(0, 7)
lf0_dm = parameter.Uniform(-9, -7)
dm_prior = utils.turnover(log10_A=log10_A_dm,
gamma=gamma_dm,
lf0=lf0_dm,
kappa=kappa_dm)
elif psd == 'tprocess':
df = 2
alphas_dm = gpp.InvGamma(df / 2, df / 2, size=components)
dm_prior = gpp.t_process(log10_A=log10_A_dm,
gamma=gamma_dm,
alphas=alphas_dm)
elif psd == 'tprocess_adapt':
df = 2
alpha_adapt_dm = gpp.InvGamma(df / 2, df / 2, size=1)
nfreq_dm = parameter.Uniform(-0.5, 10 - 0.5)
dm_prior = gpp.t_process_adapt(log10_A=log10_A_dm,
gamma=gamma_dm,
alphas_adapt=alpha_adapt_dm,
nfreq=nfreq_dm)
if psd == 'spectrum':
if prior == 'uniform':
log10_rho_dm = parameter.LinearExp(-10, -4, size=components)
elif prior == 'log-uniform':
log10_rho_dm = parameter.Uniform(-10, -4, size=components)
dm_prior = gpp.free_spectrum(log10_rho=log10_rho_dm)
dm_basis = utils.createfourierdesignmatrix_dm(nmodes=components,
Tspan=Tspan)
elif gp_kernel == 'nondiag':
if nondiag_kernel == 'periodic':
# Periodic GP kernel for DM
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
log10_p = parameter.Uniform(-4, 1)
log10_gam_p = parameter.Uniform(-3, 2)
dm_basis = gpk.linear_interp_basis_dm(dt=dt * const.day)
dm_prior = gpk.periodic_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell,
log10_gam_p=log10_gam_p,
log10_p=log10_p)
elif nondiag_kernel == 'periodic_rfband':
# Periodic GP kernel for DM with RQ radio-frequency dependence
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
log10_ell2 = parameter.Uniform(2, 7)
log10_alpha_wgt = parameter.Uniform(-4, 1)
log10_p = parameter.Uniform(-4, 1)
log10_gam_p = parameter.Uniform(-3, 2)
dm_basis = gpk.get_tf_quantization_matrix(df=df,
dt=dt * const.day,
dm=True)
dm_prior = gpk.tf_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell,
log10_gam_p=log10_gam_p,
log10_p=log10_p,
log10_alpha_wgt=log10_alpha_wgt,
log10_ell2=log10_ell2)
elif nondiag_kernel == 'sq_exp':
# squared-exponential GP kernel for DM
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
dm_basis = gpk.linear_interp_basis_dm(dt=dt * const.day)
dm_prior = gpk.se_dm_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell)
elif nondiag_kernel == 'sq_exp_rfband':
# Sq-Exp GP kernel for DM with RQ radio-frequency dependence
log10_sigma = parameter.Uniform(-10, -4)
log10_ell = parameter.Uniform(1, 4)
log10_ell2 = parameter.Uniform(2, 7)
log10_alpha_wgt = parameter.Uniform(-4, 1)
dm_basis = gpk.get_tf_quantization_matrix(df=df,
dt=dt * const.day,
dm=True)
dm_prior = gpk.sf_kernel(log10_sigma=log10_sigma,
log10_ell=log10_ell,
log10_alpha_wgt=log10_alpha_wgt,
log10_ell2=log10_ell2)
elif nondiag_kernel == 'dmx_like':
# DMX-like signal
log10_sigma = parameter.Uniform(-10, -4)
dm_basis = gpk.linear_interp_basis_dm(dt=dt * const.day)
dm_prior = gpk.dmx_ridge_prior(log10_sigma=log10_sigma)
dmgp = gp_signals.BasisGP(dm_prior,
dm_basis,
name='dm_gp',
coefficients=coefficients)
return dmgp
def red_noise_block(psd='powerlaw',
prior='log-uniform',
Tspan=None,
components=30,
gamma_val=None,
coefficients=False,
select=None,
modes=None,
wgts=None,
break_flat=False,
break_flat_fq=None):
"""
Returns red noise model:
1. Red noise modeled as a power-law with 30 sampling frequencies
:param psd:
PSD function [e.g. powerlaw (default), turnover, spectrum, tprocess]
:param prior:
Prior on log10_A. Default if "log-uniform". Use "uniform" for
upper limits.
:param Tspan:
Sets frequency sampling f_i = i / Tspan. Default will
use overall time span for indivicual pulsar.
:param components:
Number of frequencies in sampling of red noise
:param gamma_val:
If given, this is the fixed slope of the power-law for
powerlaw, turnover, or tprocess red noise
:param coefficients: include latent coefficients in GP model?
"""
# red noise parameters that are common
if psd in [
'powerlaw', 'powerlaw_genmodes', 'turnover', 'tprocess',
'tprocess_adapt', 'infinitepower'
]:
# parameters shared by PSD functions
if prior == 'uniform':
log10_A = parameter.LinearExp(-20, -11)
elif prior == 'log-uniform' and gamma_val is not None:
if np.abs(gamma_val - 4.33) < 0.1:
log10_A = parameter.Uniform(-20, -11)
else:
log10_A = parameter.Uniform(-20, -11)
else:
log10_A = parameter.Uniform(-20, -11)
if gamma_val is not None:
gamma = parameter.Constant(gamma_val)
else:
gamma = parameter.Uniform(0, 7)
# different PSD function parameters
if psd == 'powerlaw':
pl = utils.powerlaw(log10_A=log10_A, gamma=gamma)
elif psd == 'powerlaw_genmodes':
pl = gpp.powerlaw_genmodes(log10_A=log10_A, gamma=gamma, wgts=wgts)
elif psd == 'turnover':
kappa = parameter.Uniform(0, 7)
lf0 = parameter.Uniform(-9, -7)
pl = utils.turnover(log10_A=log10_A,
gamma=gamma,
lf0=lf0,
kappa=kappa)
elif psd == 'tprocess':
df = 2
alphas = gpp.InvGamma(df / 2, df / 2, size=components)
pl = gpp.t_process(log10_A=log10_A, gamma=gamma, alphas=alphas)
elif psd == 'tprocess_adapt':
df = 2
alpha_adapt = gpp.InvGamma(df / 2, df / 2, size=1)
nfreq = parameter.Uniform(-0.5, 10 - 0.5)
pl = gpp.t_process_adapt(log10_A=log10_A,
gamma=gamma,
alphas_adapt=alpha_adapt,
nfreq=nfreq)
elif psd == 'infinitepower':
pl = gpp.infinitepower()
if psd == 'spectrum':
if prior == 'uniform':
log10_rho = parameter.LinearExp(-10, -4, size=components)
elif prior == 'log-uniform':
log10_rho = parameter.Uniform(-10, -4, size=components)
pl = gpp.free_spectrum(log10_rho=log10_rho)
if select == 'backend':
# define selection by observing backend
selection = selections.Selection(selections.by_backend)
elif select == 'band' or select == 'band+':
# define selection by observing band
selection = selections.Selection(selections.by_band)
else:
# define no selection
selection = selections.Selection(selections.no_selection)
if break_flat:
log10_A_flat = parameter.Uniform(-20, -11)
gamma_flat = parameter.Constant(0)
pl_flat = utils.powerlaw(log10_A=log10_A_flat, gamma=gamma_flat)
freqs = 1.0 * np.arange(1, components + 1) / Tspan
components_low = sum(f < break_flat_fq for f in freqs)
if components_low < 1.5:
components_low = 2
rn = gp_signals.FourierBasisGP(pl,
components=components_low,
Tspan=Tspan,
coefficients=coefficients,
selection=selection)
rn_flat = gp_signals.FourierBasisGP(pl_flat,
modes=freqs[components_low:],
coefficients=coefficients,
selection=selection,
name='red_noise_hf')
rn = rn + rn_flat
else:
rn = gp_signals.FourierBasisGP(pl,
components=components,
Tspan=Tspan,
coefficients=coefficients,
selection=selection,
modes=modes)
if select == 'band+': # Add the common component as well
rn = rn + gp_signals.FourierBasisGP(
pl, components=components, Tspan=Tspan, coefficients=coefficients)
return rn
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
######################
bkend = selections.Selection(selections.by_backend)
bkend_NG = selections.Selection(selections.nanograv_backends)
# fix white noise parameters
efac = parameter.Constant()
equad = parameter.Constant()
ecorr = parameter.Constant()
# DMGP parameters and powerlaw
dm_log10_A = parameter.Uniform(-20, -11)
dm_gamma = parameter.Uniform(0, 7)
if args.use_dmto:
dm_kappa = parameter.Uniform(0, 7)
dm_lf0 = parameter.Uniform(-9, -7)
dm_pl = utils.turnover(log10_A=dm_log10_A, gamma=dm_gamma,
lf0=dm_lf0, kappa=dm_kappa)
else:
dm_pl = utils.powerlaw(log10_A=dm_log10_A, gamma=dm_gamma)
dm_basis = utils.createfourierdesignmatrix_dm(nmodes=30, Tspan=Tspan)
# red noise parameters and powerlaw
if args.ul:
rn_log10_A = parameter.LinearExp(-20, -11)
else:
rn_log10_A = parameter.Uniform(-20, -11)
rn_gamma = parameter.Uniform(0, 7)
rn_pl = utils.powerlaw(log10_A=rn_log10_A, gamma=rn_gamma)
# GWB parameters and powerlaw
orf = utils.hd_orf()
if args.ul:
