def test_broken_powerlaw_prior(self):
"""Test that red noise signal returns correct values."""
# set up signal parameter
pr = gp_priors.broken_powerlaw(
log10_A=parameter.Uniform(-18, -12),
gamma=parameter.Uniform(1, 7),
log10_fb=parameter.Uniform(-9, -7.5),
kappa=parameter.Uniform(0.1, 1.0),
delta=parameter.Uniform(0.01, 1),
)
basis = gp_bases.createfourierdesignmatrix_red(nmodes=30)
rn = gp_signals.BasisGP(priorFunction=pr,
basisFunction=basis,
name="red_noise")
rnm = rn(self.psr)
# parameters
log10_A, gamma, log10_fb, kappa, delta = -14.5, 4.33, -8.5, 1, 0.5
params = {
"B1855+09_red_noise_log10_A": log10_A,
"B1855+09_red_noise_gamma": gamma,
"B1855+09_red_noise_log10_fb": log10_fb,
"B1855+09_red_noise_kappa": kappa,
"B1855+09_red_noise_delta": delta,
}
# basis matrix test
F, f2 = gp_bases.createfourierdesignmatrix_red(self.psr.toas,
nmodes=30)
msg = "F matrix incorrect for turnover."
assert np.allclose(F, rnm.get_basis(params)), msg
# spectrum test
phi = gp_priors.broken_powerlaw(f2,
log10_A=log10_A,
gamma=gamma,
log10_fb=log10_fb,
kappa=kappa,
delta=delta)
msg = "Spectrum incorrect for turnover."
assert np.all(rnm.get_phi(params) == phi), msg
# inverse spectrum test
msg = "Spectrum inverse incorrect for turnover."
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 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 common_red_noise_block(psd='powerlaw', prior='log-uniform',
Tspan=None, components=30,
gamma_val=None, delta_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', '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 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 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()}
# common red noise parameters
if psd in ['powerlaw', 'turnover', 'turnover_knee','broken_powerlaw']:
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 == '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