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 = 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 test_powerlaw_genmodes_prior(self):
"""Test that red noise signal returns correct values."""
# set up signal parameter
pr = gp_priors.powerlaw_genmodes(log10_A=parameter.Uniform(-18, -12),
gamma=parameter.Uniform(1, 7))
basis = gp_bases.createfourierdesignmatrix_chromatic(nmodes=30)
rn = gp_signals.BasisGP(priorFunction=pr,
basisFunction=basis,
name="red_noise")
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 = gp_bases.createfourierdesignmatrix_chromatic(self.psr.toas,
self.psr.freqs,
nmodes=30)
msg = "F matrix incorrect for turnover."
assert np.allclose(F, rnm.get_basis(params)), msg
# spectrum test
phi = gp_priors.powerlaw_genmodes(f2, log10_A=log10_A, gamma=gamma)
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 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 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