def run_mcmc_1d(t, data, logS0_init,
logw0_init, logQ_init,
logsig_init, t0_init,
r_init, d_init, tin_init):
with pm.Model() as model:
#logsig = pm.Uniform("logsig", lower=-20.0, upper=0.0, testval=logsig_init)
# The parameters of the SHOTerm kernel
#logS0 = pm.Uniform("logS0", lower=-50.0, upper=0.0, testval=logS0_init)
#logQ = pm.Uniform("logQ", lower=-50.0, upper=20.0, testval=logQ_init)
#logw0 = pm.Uniform("logw0", lower=-50.0, upper=20.0, testval=logw0_init)
# The parameters for the transit mean function
t0 = pm.Uniform("t0", lower=t[0], upper=t[-1], testval=t0_init)
r = pm.Uniform("r", lower=0.0, upper=1.0, testval=r_init)
d = pm.Uniform("d", lower=0.0, upper=10.0, testval=d_init)
tin = pm.Uniform("tin", lower=0.0, upper=10.0, testval=tin_init)
# Deterministics
# mean = pm.Deterministic("mean", utils.transit(t, t0, r, d, tin))
transit = utils.theano_transit(t, t0, r, d, tin)
# Set up the Gaussian Process model
kernel = xo.gp.terms.SHOTerm(
log_S0 = logS0_init,
log_w0 = logw0_init,
log_Q=logQ_init
)
diag = np.exp(2*logsig_init)*tt.ones((1, len(t)))
gp = GP(kernel, t, diag, J=2)
# Compute the Gaussian Process likelihood and add it into the
# the PyMC3 model as a "potential"
pm.Potential("loglike", gp.log_likelihood(data - transit))
# Compute the mean model prediction for plotting purposes
#pm.Deterministic("mu", gp.predict())
map_soln = xo.optimize(start=model.test_point, verbose=False)
with model:
map_soln = xo.optimize(start=model.test_point)
with model:
trace = pm.sample(
tune=500,
draws=500,
start=map_soln,
cores=2,
chains=2,
step=xo.get_dense_nuts_step(target_accept=0.9),
)
return trace
def run_optimizer(pm_model, return_logl=False):
with pm_model:
map_params = xo.optimize(start=pm_model.test_point, vars=pm_model.m_b)
map_params = xo.optimize(start=map_params, vars=[pm_model.ln_delta_t0])
map_params = xo.optimize(
start=map_params,
vars=[pm_model.ln_delta_t0, pm_model.ln_A0, pm_model.ln_tE],
)
map_params, info = xo.optimize(start=map_params, return_info=True)
if return_logl == True:
return map_params, info.fun
else:
return map_params
def granulation_model(self):
peak = self.period_prior()
x = self.lc.lcf.time
y = self.lc.lcf.flux
yerr = self.lc.lcf.flux_err
with pm.Model() as model:
# The mean flux of the time series
mean = pm.Normal("mean", mu=0.0, sd=10.0)
# A jitter term describing excess white noise
logs2 = pm.Normal("logs2", mu=2*np.log(np.min(sigmaclip(yerr)[0])), sd=1.0)
logw0 = pm.Bound(pm.Normal, lower=-0.5, upper=np.log(2 * np.pi / self.min_period))("logw0", mu=0.0, sd=5)
logSw4 = pm.Normal("logSw4", mu=np.log(np.var(y)), sd=5)
kernel = xo.gp.terms.SHOTerm(log_Sw4=logSw4, log_w0=logw0, Q=1 / np.sqrt(2))
#GP model
gp = xo.gp.GP(kernel, x, yerr**2 + tt.exp(logs2))
# Compute the Gaussian Process likelihood and add it into the
# the PyMC3 model as a "potential"
pm.Potential("loglike", gp.log_likelihood(y - mean))
# Compute the mean model prediction for plotting purposes
pm.Deterministic("pred", gp.predict())
# Optimize to find the maximum a posteriori parameters
map_soln = xo.optimize(start=model.test_point)
return model, map_soln
def singleband_gp(self, lower=5, upper=50, seed=42):
# x, y, yerr = make_data_nice(x, y, yerr)
np.random.seed(seed)
with pm.Model() as model:
# The mean flux of the time series
mean = pm.Normal("mean", mu=0.0, sd=10.0)
# A jitter term describing excess white noise
logs2 = pm.Normal("logs2",
mu=2 * np.log(np.mean(self.yerr)),
sd=2.0)
# A term to describe the non-periodic variability
logSw4 = pm.Normal("logSw4", mu=np.log(np.var(self.y)), sd=5.0)
logw0 = pm.Normal("logw0", mu=np.log(2 * np.pi / 10), sd=5.0)
# The parameters of the RotationTerm kernel
logamp = pm.Normal("logamp", mu=np.log(np.var(self.y)), sd=5.0)
BoundedNormal = pm.Bound(pm.Normal,
lower=np.log(lower),
upper=np.log(upper))
logperiod = BoundedNormal("logperiod",
mu=np.log(self.init_period),
sd=5.0)
logQ0 = pm.Normal("logQ0", mu=1.0, sd=10.0)
logdeltaQ = pm.Normal("logdeltaQ", mu=2.0, sd=10.0)
mix = xo.distributions.UnitUniform("mix")
# Track the period as a deterministic
period = pm.Deterministic("period", tt.exp(logperiod))
# Set up the Gaussian Process model
kernel = xo.gp.terms.SHOTerm(log_Sw4=logSw4,
log_w0=logw0,
Q=1 / np.sqrt(2))
kernel += xo.gp.terms.RotationTerm(log_amp=logamp,
period=period,
log_Q0=logQ0,
log_deltaQ=logdeltaQ,
mix=mix)
gp = xo.gp.GP(kernel,
self.x,
self.yerr**2 + tt.exp(logs2),
mean=mean)
# Compute the Gaussian Process likelihood and add it into the
# the PyMC3 model as a "potential"
gp.marginal("gp", observed=self.y)
# Compute the mean model prediction for plotting purposes
pm.Deterministic("pred", gp.predict())
# Optimize to find the maximum a posteriori parameters
map_soln = xo.optimize(start=model.test_point)
self.model = model
self.map_soln = model
return map_soln, model
def run_pymc3_model(pos, pos_err, proper, proper_err, mean, cov):
M = get_tangent_basis(pos[0] * 2 * np.pi / 360, pos[1] * 2 * np.pi / 360)
# mean, cov = get_prior()
with pm.Model() as model:
vxyzD = pm.MvNormal("vxyzD", mu=mean, cov=cov, shape=4)
vxyz = pm.Deterministic("vxyz", vxyzD[:3])
log_D = pm.Deterministic("log_D", vxyzD[3])
D = pm.Deterministic("D", tt.exp(log_D))
xyz = pm.Deterministic("xyz", tt_eqtogal(pos[0], pos[1], D)[:, 0])
pm_from_v, rv_from_v = tt_get_icrs_from_galactocentric(
xyz, vxyz, pos[0], pos[1], D, M)
pm.Normal("proper_motion",
mu=pm_from_v,
sigma=np.array(proper_err),
observed=np.array(proper))
pm.Normal("parallax", mu=1. / D, sigma=pos_err[2], observed=pos[2])
map_soln = xo.optimize()
trace = pm.sample(tune=1500,
draws=1000,
start=map_soln,
step=xo.get_dense_nuts_step(target_accept=0.9))
return trace
def fit_ttv(self, n, run_MCMC=False, ttv_start=None, verbose=True):
"""
Fit a single transit with a transit timing variation, using the shape given by best-fit orbital parameters.
"""
if verbose: print("Fitting ttv for transit number", n)
# Get the transit lightcurve
transit = self.lightcurve.get_transit(n, self.p_ref, self.t0_ref)
t = transit.time * self.p_ref
y = transit.flux
sd = transit.flux_err
if ttv_start is None:
ttv_start = np.median(self.pars['ttvs'])
with pm.Model() as model:
ttv = pm.Normal("ttv", mu=ttv_start, sd=0.025) # sd = 36 minutes
orbit = xo.orbits.KeplerianOrbit(period=self.p_ref,
t0=ttv,
b=self.pars['b'])
light_curves = xo.LimbDarkLightCurve(
self.pars['u']).get_light_curve(orbit=orbit,
r=self.pars['r'],
t=t)
light_curve = pm.math.sum(light_curves, axis=-1) + 1
pm.Deterministic("transit_" + str(n), light_curve)
pm.Normal("obs", mu=light_curve, sd=sd, observed=y)
map_soln = xo.optimize(start=model.test_point,
verbose=False,
progress_bar=False)
self.pars['ttvs'][n] = float(map_soln['ttv'])
if verbose: print(f"\t ttv {n} = {self.pars['ttvs'][n]}")
if run_MCMC:
np.random.seed(42)
with model:
trace = pm.sample(
tune=500,
draws=500,
start=map_soln,
cores=1,
chains=2,
step=xo.get_dense_nuts_step(target_accept=0.9),
)
self.pars['ttvs'][n] = np.median(trace['ttv'])
self.pars['e_ttvs'][n] = self.pars['ttvs'][n] - np.percentile(
trace['ttv'], 16, axis=0)
self.pars['E_ttvs'][n] = -self.pars['ttvs'][n] + np.percentile(
trace['ttv'], 84, axis=0)
if verbose:
print(
f"\t ttv {n} = {self.pars['ttvs'][n]} /+ {self.pars['E_ttvs'][n]} /- {self.pars['e_ttvs'][n]}"
)
def gp_fit(t, y, yerr, t_grid, integrated=False, exp_time=60.):
# optimize kernel hyperparameters and return fit + predictions
with pm.Model() as model:
logS0 = pm.Normal("logS0", mu=0.4, sd=5.0, testval=np.log(np.var(y)))
logw0 = pm.Normal("logw0", mu=-3.9, sd=0.1)
logQ = pm.Normal("logQ", mu=3.5, sd=5.0)
# Set up the kernel and GP
kernel = terms.SHOTerm(log_S0=logS0, log_w0=logw0, log_Q=logQ)
if integrated:
kernel_int = terms.IntegratedTerm(kernel, exp_time)
gp = GP(kernel_int, t, yerr**2)
else:
gp = GP(kernel, t, yerr**2)
# Add a custom "potential" (log probability function) with the GP likelihood
pm.Potential("gp", gp.log_likelihood(y))
with model:
map_soln = xo.optimize(start=model.test_point)
mu, var = xo.eval_in_model(gp.predict(t_grid, return_var=True),
map_soln)
sd = np.sqrt(var)
y_pred = xo.eval_in_model(gp.predict(t), map_soln)
return map_soln, mu, sd, y_pred
def get_map_soln(model, verbose=False, ignore_warnings=True):
"""
Get the maximum a posteriori probability estimate of the parameters.
Parameters
----------
model : `~pymc3.model`
The model object.
verbose : bool, optional
Print details of optimization.
ignore_warnings : bool, optional
Silence warnings.
Returns
-------
map_soln : dict
A dictionary with the maximum a posteriori estimates of the variables.
"""
# Ignore warnings from theano, unless specified elsewise
if ignore_warnings:
warnings.filterwarnings(action='ignore',
category=FutureWarning,
module='theano')
with model:
# Fit for the maximum a posteriori parameters
map_soln = xo.optimize(start=model.test_point, verbose=verbose)
map_soln = xo.optimize(
start=map_soln,
vars=[model.f0, model.period, model.t0, model.r],
verbose=verbose)
map_soln = xo.optimize(start=map_soln,
vars=model.rho_star,
verbose=verbose)
map_soln = xo.optimize(start=map_soln, vars=model.t14, verbose=verbose)
map_soln = xo.optimize(start=map_soln, verbose=verbose)
# Reset warning filter
warnings.resetwarnings()
return map_soln
def loglike(t0):
print("t0={0}".format(t0))
h = copy.deepcopy(holds)
h['t0m'] = t0
m = getmodel(holds=h, mu=mu, sig=sig)
with m:
newmap_soln = xo.optimize(start=start, verbose=False)
ll = m.logp(newmap_soln)
#r[i] = np.exp(newmap_soln['logrm'])
return ll
def find_optimum(self):
"""
Optimize to find the MAP solution.
Returns:
map_soln (dict): a dictionary containing the optimized parameters.
"""
with self.model:
map_soln = xo.optimize(start=self.model.test_point)
self.map_soln = map_soln
success = True
if self.map_soln["step1"] == self.steps[0]:
sucess = False
return map_soln, success
def rotation_model(self):
peak = self.period_prior()
x = self.lc.lcf.time
y = self.lc.lcf.flux
yerr = self.lc.lcf.flux_err
with pm.Model() as model:
# The mean flux of the time series
mean = pm.Normal("mean", mu=0.0, sd=10.0)
# A jitter term describing excess white noise
logs2 = pm.Normal("logs2",
mu=2 * np.log(np.min(sigmaclip(yerr)[0])),
sd=1.0)
# The parameters of the RotationTerm kernel
logamp = pm.Normal("logamp", mu=np.log(np.var(y)), sd=5.0)
logperiod = pm.Bound(pm.Normal,
lower=np.log(self.min_period),
upper=np.log(self.max_period))(
"logperiod",
mu=np.log(peak["period"]),
sd=2.0)
logQ0 = pm.Uniform("logQ0", lower=-15, upper=5)
logdeltaQ = pm.Uniform("logdeltaQ", lower=-15, upper=5)
mix = pm.Uniform("mix", lower=0, upper=1.0)
# Track the period as a deterministic
period = pm.Deterministic("period", tt.exp(logperiod))
kernel = xo.gp.terms.RotationTerm(log_amp=logamp,
period=period,
log_Q0=logQ0,
log_deltaQ=logdeltaQ,
mix=mix)
gp = xo.gp.GP(kernel, x, yerr**2 + tt.exp(logs2), J=4)
# Compute the Gaussian Process likelihood and add it into the
# the PyMC3 model as a "potential"
pm.Potential("loglike", gp.log_likelihood(y - mean))
# Compute the mean model prediction for plotting purposes
pm.Deterministic("pred", gp.predict())
# Optimize to find the maximum a posteriori parameters
map_soln = xo.optimize(start=model.test_point)
return model, map_soln
period=period,
log_Q0=logQ0,
log_deltaQ=logdQ,
mix=mix
)
kernel += xo.gp.terms.SHOTerm(
log_S0 = logS0,
log_w0 = logw,
log_Q = -np.log(np.sqrt(2))
)
gp = xo.gp.GP(kernel, x, yerr**2 * np.ones_like(x), mean=mean, J=6)
gp.marginal("gp", observed = y)
start = model.test_point
map_soln = xo.optimize(start=start, verbose=True)
trace = pm.sample(
tune=1000,
draws=500,
start=start,
cores=28,
chains=28,
step=xo.get_dense_nuts_step(target_accept=0.9),
progressbar=False
)
plotting.cornerplot(lc, trace, 'EPIC', smooth=True, truth_color=red);
pl.savefig("{0}/{1}".format(outdir, cornerfile), dpi=200)
acf_kwargs = {'color': 'k', 'linewidth': 3}
pk_kwargs = {'color': red, 'linewidth': 1, 'linestyle': '--'}
def worker(task):
(i1, i2), data, model_kw, basename = task
g = GaiaData(data)
cache_filename = os.path.abspath(f'../cache/tmp-{basename}_{i1}-{i2}.fits')
if os.path.exists(cache_filename):
print(f"({pid}) cache filename exists for index range: "
f"{cache_filename}")
return cache_filename
print(f"({pid}) setting up model")
helper = ComovingHelper(g)
niter = 0
while niter < 10:
try:
model = helper.get_model(**model_kw)
break
except OSError:
print(f"{pid} failed to compile - trying again in 2sec...")
time.sleep(5)
niter += 1
continue
else:
print(f"{pid} never successfully compiled. aborting")
import socket
print(socket.gethostname(), socket.getfqdn(),
os.path.exists("/cm/shared/sw/pkg/devel/gcc/7.4.0/bin/g++"))
return ''
print(f"({pid}) done init model - running {len(g)} stars")
probs = np.full(helper.N, np.nan)
for n in range(helper.N):
with model:
pm.set_data({
'y': helper.ys[n],
'Cinv': helper.Cinvs[n],
'M': helper.Ms[n]
})
test_pt = {
'vxyz': helper.test_vxyz[n],
'r': helper.test_r[n],
'w': np.array([0.5, 0.5])
}
try:
print("starting optimize")
res = xo.optimize(start=test_pt,
progress_bar=False,
verbose=False)
print("done optimize - starting sample")
trace = pm.sample(
start=res,
tune=2000,
draws=1000,
cores=1,
chains=1,
step=xo.get_dense_nuts_step(target_accept=0.95),
progressbar=False)
except Exception as e:
print(str(e))
continue
# print("done sample - computing prob")
ll_fg = trace.get_values(model.group_logp)
ll_bg = trace.get_values(model.field_logp)
post_prob = np.exp(ll_fg - np.logaddexp(ll_fg, ll_bg))
probs[n] = post_prob.sum() / len(post_prob)
# write probs to cache filename
tbl = at.Table()
tbl['source_id'] = g.source_id
tbl['prob'] = probs
tbl.write(cache_filename)
return cache_filename
def run_fitting():
times = self.light_curve_data_source.data['Time (BTJD)'].astype(
np.float32)
flux_errors = self.light_curve_data_source.data[
'Normalized PDCSAP flux error']
fluxes = self.light_curve_data_source.data[
'Normalized PDCSAP flux']
relative_times = self.light_curve_data_source.data['Time (days)']
nan_indexes = np.union1d(
np.argwhere(np.isnan(fluxes)),
np.union1d(np.argwhere(np.isnan(times)),
np.argwhere(np.isnan(flux_errors))))
fluxes = np.delete(fluxes, nan_indexes)
flux_errors = np.delete(flux_errors, nan_indexes)
times = np.delete(times, nan_indexes)
relative_times = np.delete(relative_times, nan_indexes)
with pm.Model() as model:
# Stellar parameters
mean = pm.Normal("mean", mu=0.0, sigma=10.0 * 1e-3)
u = xo.distributions.QuadLimbDark("u")
star_params = [mean, u]
# Gaussian process noise model
sigma = pm.InverseGamma("sigma",
alpha=3.0,
beta=2 * np.nanmedian(flux_errors))
log_Sw4 = pm.Normal("log_Sw4", mu=0.0, sigma=10.0)
log_w0 = pm.Normal("log_w0",
mu=np.log(2 * np.pi / 10.0),
sigma=10.0)
kernel = xo.gp.terms.SHOTerm(log_Sw4=log_Sw4,
log_w0=log_w0,
Q=1.0 / 3)
noise_params = [sigma, log_Sw4, log_w0]
# Planet parameters
log_ror = pm.Normal("log_ror",
mu=0.5 * np.log(self_.depth),
sigma=10.0 * 1e-3)
ror = pm.Deterministic("ror", tt.exp(log_ror))
depth = pm.Deterministic('Transit depth (relative flux)',
tt.square(ror))
planet_radius = pm.Deterministic('Planet radius (solar radii)',
ror * self_.star_radius)
# Orbital parameters
log_period = pm.Normal("log_period",
mu=np.log(self_.period),
sigma=1.0)
t0 = pm.Normal('Transit epoch (BTJD)',
mu=self_.transit_epoch,
sigma=1.0)
log_dur = pm.Normal("log_dur", mu=np.log(0.1), sigma=10.0)
b = xo.distributions.ImpactParameter("b", ror=ror)
period = pm.Deterministic('Transit period (days)',
tt.exp(log_period))
dur = pm.Deterministic('Transit duration (days)',
tt.exp(log_dur))
# Set up the orbit
orbit = xo.orbits.KeplerianOrbit(period=period,
duration=dur,
t0=t0,
b=b,
r_star=self.star_radius)
# We're going to track the implied density for reasons that will become clear later
pm.Deterministic("rho_circ", orbit.rho_star)
# Set up the mean transit model
star = xo.LimbDarkLightCurve(u)
def lc_model(t):
return mean + tt.sum(star.get_light_curve(
orbit=orbit, r=ror * self.star_radius, t=t),
axis=-1)
# Finally the GP observation model
gp = xo.gp.GP(kernel,
times, (flux_errors**2) + (sigma**2),
mean=lc_model)
gp.marginal("obs", observed=fluxes)
# Double check that everything looks good - we shouldn't see any NaNs!
print(model.check_test_point())
# Optimize the model
map_soln = model.test_point
map_soln = xo.optimize(map_soln, [sigma])
map_soln = xo.optimize(map_soln, [log_ror, b, log_dur])
map_soln = xo.optimize(map_soln, noise_params)
map_soln = xo.optimize(map_soln, star_params)
map_soln = xo.optimize(map_soln)
with model:
gp_pred, lc_pred = xo.eval_in_model(
[gp.predict(), lc_model(times)], map_soln)
x_fold = (times - map_soln['Transit epoch (BTJD)'] +
0.5 * map_soln['Transit period (days)']
) % map_soln['Transit period (days)'] - 0.5 * map_soln[
'Transit period (days)']
inds = np.argsort(x_fold)
bokeh_document.add_next_tick_callback(
partial(update_initial_fit_figure, fluxes, gp_pred, inds,
lc_pred, map_soln, relative_times, times, x_fold))
self.bokeh_document.add_next_tick_callback(
partial(fit, self, map_soln, model))
plt.plot(t, xo.eval_in_model(model.bkg_pred), ":k", alpha=0.5)
plt.plot(t, xo.eval_in_model(model.rv_model_pred), label="model")
plt.legend(fontsize=10)
plt.xlim(t.min(), t.max())
plt.xlabel("time [days]")
plt.ylabel("radial velocity [m/s]")
_ = plt.title("initial model")
# -
# In this plot, the background is the dotted line, the individual planets are the dashed lines, and the full model is the blue line.
#
# It doesn't look amazing so let's fit for the maximum a posterior parameters.
with model:
map_soln = xo.optimize(start=model.test_point, vars=[trend])
map_soln = xo.optimize(start=map_soln)
# +
plt.errorbar(x, y, yerr=yerr, fmt=".k")
plt.plot(t, map_soln["vrad_pred"], "--k", alpha=0.5)
plt.plot(t, map_soln["bkg_pred"], ":k", alpha=0.5)
plt.plot(t, map_soln["rv_model_pred"], label="model")
plt.legend(fontsize=10)
plt.xlim(t.min(), t.max())
plt.xlabel("time [days]")
plt.ylabel("radial velocity [m/s]")
_ = plt.title("MAP model")
# -
def spectrum_theano_model(obs):
""" Build a spectrum estimate, old theano model """
dat = (obs.data / obs.basic_model)
dat /= obs.vsr_grad_model
err = (obs.error / obs.basic_model)
err /= obs.vsr_grad_model
y = (dat).ravel()
ye = (err).ravel()
ye[obs.cosmic_rays.ravel()] = 1e10
ye[ye / y > 0.01] = 1e10
ye[ye < 1e-4] = 1e10
in_transit = obs.in_transit
xshift = obs.xshift
xshift -= np.mean(xshift)
xshift /= (np.max(xshift) - np.min(xshift))
xshift = np.atleast_3d(xshift).transpose([1, 0, 2]) * np.ones(
obs.data.shape)
# This will help us mask the transit later.
cadence_mask = (np.atleast_3d(~in_transit).transpose([1, 0, 2]) *
np.ones(obs.data.shape, bool)).ravel()
with pm.Model() as model:
# Track each dimension in theano tensors
X_t = tt.as_tensor(obs.X[~in_transit]).flatten()
Y_t = tt.as_tensor(obs.Y[~in_transit]).flatten()
T_t = tt.as_tensor(obs.T[~in_transit]).flatten()
xshift_t = tt.as_tensor(xshift[~in_transit]).flatten()
g_spat_t = tt.as_tensor(
(np.atleast_3d(obs.spec_grad_simple).transpose([0, 2, 1]) *
np.ones(obs.data.shape))[~in_transit]).flatten()
# Stellar spectrum gradient
sg = pm.Normal("spectrum_gradient",
mu=obs.spec_grad_simple,
sd=np.ones(obs.data.shape[2]) * 1,
testval=obs.spec_grad_simple,
shape=obs.data.shape[2])
# Reshaping to the correct dimensions of the image
sg_3d = sg + tt.zeros(obs.data[~in_transit].shape)
sg_flat = sg_3d.flatten()
# Design matrix with all the shifts and tilts
A = tt.stack([
# Zeropoints and trends
Y_t,
T_t,
Y_t * X_t,
Y_t * X_t * T_t,
# Spectrum tilts
sg_flat,
sg_flat * Y_t,
sg_flat * X_t * Y_t,
# Spectrum shifts
sg_flat * xshift_t,
sg_flat * xshift_t**2,
sg_flat * xshift_t * X_t,
# Spectrum stretches
tt.abs_(sg_flat) * Y_t,
tt.abs_(sg_flat) * xshift_t * X_t,
tt.ones_like(sg_flat),
]).T
# Linear algebra to find the best fitting shifts
sigma_w_inv = A.T.dot(A / ye[cadence_mask, None]**2)
B = A.T.dot((y[cadence_mask] / ye[cadence_mask]**2))
w = pm.Deterministic('w', tt.slinalg.solve(sigma_w_inv, B))
y_model = A.dot(w)
pm.Normal("obs",
mu=y_model,
sd=ye[cadence_mask],
observed=y[cadence_mask])
# Optimize to find the best fitting spectral gradient
map_soln = xo.optimize(start=model.test_point, vars=[sg])
sg_n = (np.atleast_3d(map_soln['spectrum_gradient']) *
np.ones(dat.shape).transpose([0, 2, 1])).transpose([0, 2, 1])
A = np.vstack([
obs.Y.ravel(),
obs.T.ravel(),
obs.Y.ravel() * obs.X.ravel(),
obs.Y.ravel() * obs.X.ravel() * obs.T.ravel(),
sg_n.ravel(), (sg_n * obs.Y).ravel(), (sg_n * obs.X * obs.Y).ravel(),
(sg_n * xshift).ravel(), (sg_n * xshift**2).ravel(),
(sg_n * xshift * obs.Y).ravel(), (np.abs(sg_n) * obs.Y).ravel(),
(np.abs(sg_n) * obs.Y * xshift).ravel(),
np.ones(np.product(dat.shape))
]).T
model_n = A.dot(map_soln['w']).reshape(obs.data.shape)
return model_n
def hybrid_model(self):
def submodel1(x, y, yerr, parent):
with pm.Model(name="rotation_", model=parent) as submodel:
# The mean flux of the time series
mean1 = pm.Normal("mean1", mu=0.0, sd=10.0)
# A jitter term describing excess white noise
logs21 = pm.Normal("logs21", mu=np.log(np.mean(yerr)), sd=2.0)
# The parameters of the RotationTerm kernel
logamp = pm.Normal("logamp", mu=np.log(np.var(y)), sd=5.0)
#logperiod = pm.Uniform("logperiod", lower=np.log(vgp.min_period), upper=np.log(vgp.max_period))
logperiod = pm.Bound(pm.Normal,
lower=np.log(self.min_period),
upper=np.log(self.max_period))(
"logperiod",
mu=np.log(peak["period"]),
sd=1.0)
logQ0 = pm.Uniform("logQ0", lower=-15, upper=5)
logdeltaQ = pm.Uniform("logdeltaQ", lower=-15, upper=5)
mix = pm.Uniform("mix", lower=0, upper=1.0)
# Track the period as a deterministic
period = pm.Deterministic("period", tt.exp(logperiod))
kernel1 = xo.gp.terms.RotationTerm(log_amp=logamp,
period=period,
log_Q0=logQ0,
log_deltaQ=logdeltaQ,
mix=mix)
gp1 = xo.gp.GP(kernel1, x, yerr**2 + tt.exp(logs21))
# Compute the Gaussian Process likelihood and add it into the
# the PyMC3 model as a "potential"
loglike1 = gp1.log_likelihood(y - mean1)
#pred1 = pm.Deterministic("pred1", gp1.predict())
return logperiod, logQ0, gp1, loglike1
def submodel2(x, y, yerr, parent):
with pm.Model(name="granulation", model=parent) as submodel:
# The parameters of SHOTerm kernel for non-periodicity granulation
mean2 = pm.Normal("mean2", mu=0.0, sd=10.0)
#logz = pm.Uniform("logz", lower=np.log(2 * np.pi / 4), upper=np.log(2*np.pi/vgp.min_period))
#sigma = pm.HalfCauchy("sigma", 3.0)
#logw0 = pm.Normal("logw0", mu=logz, sd=2.0)
logw0 = pm.Bound(pm.Normal,
lower=np.log(2 * np.pi / 2.5),
upper=np.log(2 * np.pi / self.min_period))(
"logw0", mu=np.log(2 * np.pi / 0.8), sd=1)
logSw4 = pm.Normal("logSw4",
mu=np.log(np.var(y) * (2 * np.pi / 2)**4),
sd=5)
logs22 = pm.Normal("logs22", mu=np.log(np.mean(yerr)), sd=2.0)
logQ = pm.Bound(pm.Normal,
lower=np.log(1 / 2),
upper=np.log(2))("logQ",
mu=np.log(1 / np.sqrt(2)),
sd=1)
kernel2 = xo.gp.terms.SHOTerm(log_Sw4=logSw4,
log_w0=logw0,
log_Q=logQ)
gp2 = xo.gp.GP(kernel2, x, yerr**2 + tt.exp(logs22))
loglike2 = gp2.log_likelihood(y - mean2)
return logw0, logQ, gp2, loglike2
peak = self.period_prior()
x = self.lc.lcf.time
y = self.lc.lcf.flux
yerr = self.lc.lcf.flux_err
y1_old = self.lc.lcf.flatten(window_length=self.window_width,
return_trend=True)[1].flux
y2_old = y - y1_old
y2 = sigmaclip(y2_old)[0]
idx = np.in1d(y2_old, y2)
self.y_new = y[idx]
self.yerr_new = yerr[idx]
self.x_new = x[idx]
y1_old_ave = np.nanmean(y1_old[idx])
#y1_old_std = np.nanstd(y1_old[idx])
self.y1 = (y1_old[idx] - y1_old_ave) * 1e6
self.y1_err = window_rms(yerr, self.window_width)[idx] * 1e6
#y1 = y1[idx]
y2_old = self.y_new - y1_old[idx]
y2_old_ave = np.nanmean(y2_old)
#y2_old_std = np.nanstd(y2_old)
self.y2 = (y2_old - y2_old_ave) * 1e6 #/y2_old_ave
y2_err = np.sqrt(self.yerr_new**2 -
window_rms(yerr, self.window_width)[idx]**2)
y2_err[np.isnan(y2_err)] = 0
self.y2_err = y2_err * 1e6 #/ y2_old_ave
#y2 = self.lc.lcf.flatten(window_length=401, return_trend=False).flux
y_class = [self.y1, self.y2]
yerr_class = [self.y1_err, self.y2_err]
submodel_class = [submodel1, submodel2]
with pm.Model() as model:
gp_class = []
loglikes = []
logtaus = []
logQs = []
for i in range(1, 3):
logtau, log_Q, gp, loglike = submodel_class[i - 1](
self.x_new, y_class[i - 1], yerr_class[i - 1], model)
gp_class.append(gp)
loglikes.append(loglike)
logtaus.append(logtau)
logQs.append(log_Q)
#loglikes = tt.stack(loglikes)
#pm.Potential("loglike", pm.math.logsumexp(loglikes))
pm.Potential("loglike_rot", loglikes[0])
pm.Potential("loglike_gra", loglikes[1])
predrot = pm.Deterministic(
"pred_rot", gp_class[0].predict() / 1e6 + y1_old_ave)
predgra = pm.Deterministic(
"pred_gra", gp_class[1].predict() / 1e6 + y2_old_ave)
predtot = pm.Deterministic(
"pred_tot", gp_class[0].predict() / 1e6 + y1_old_ave +
gp_class[1].predict() / 1e6 + y2_old_ave)
# Optimize to find the maximum a posteriori parameters
map_soln = xo.optimize(start=model.test_point,
vars=[logtaus[0], logQs[0]])
map_soln = xo.optimize(start=model.test_point,
vars=[logtaus[1], logQs[1]])
map_soln = xo.optimize(start=model.test_point)
return model, map_soln
import pymc3 as pm
import exoplanet as xo
import os
import src.close.rv_astro_more.model as m
with m.model:
map_sol = xo.optimize(vars=[m.a_ang, m.MAb, m.incl])
print(map_sol)
map_sol1 = xo.optimize(start=map_sol, vars=[m.incl, m.Omega])
print(map_sol1)
with m.model:
trace = pm.sample(
tune=2500,
draws=3000,
# start=map_sol,
chains=4,
step=xo.get_dense_nuts_step(target_accept=0.9),
)
chaindir = "chains/close/rv_astro_more/"
if not os.path.isdir(chaindir):
os.makedirs(chaindir)
# save the samples as a pymc3 object
pm.save_trace(trace, directory=chaindir, overwrite=True)
# and as a CSV, just in case the model spec
# changes and we have trouble reloading things
def gp_rotation(self,
init_period=None,
tune=2000,
draws=2000,
prediction=True,
cores=None):
"""
Calculate a rotation period using a Gaussian process method.
Args:
init_period (Optional[float]): Your initial guess for the rotation
period. The default is the Lomb-Scargle period.
tune (Optional[int]): The number of tuning samples. Default is
2000.
draws (Optional[int]): The number of samples. Default is 2000.
prediction (Optional[Bool]): If true, a prediction will be
calculated for each sample. This is useful for plotting the
prediction but will slow down the whole calculation.
cores (Optional[int]): The number of cores to use. Default is
None (for running one process).
Returns:
gp_period (float): The GP rotation period in days.
errp (float): The upper uncertainty on the rotation period.
errm (float): The lower uncertainty on the rotation period.
logQ (float): The Q factor.
Qerrp (float): The upper uncertainty on the Q factor.
Qerrm (float): The lower uncertainty on the Q factor.
"""
self.prediction = prediction
x = np.array(self.time, dtype=float)
# Median of data must be zero
y = np.array(self.flux, dtype=float) - np.median(self.flux)
yerr = np.array(self.flux_err, dtype=float)
if init_period is None:
# Calculate ls period
init_period = self.ls_rotation()
with pm.Model() as model:
# The mean flux of the time series
mean = pm.Normal("mean", mu=0.0, sd=10.0)
# A jitter term describing excess white noise
logs2 = pm.Normal("logs2", mu=2 * np.log(np.min(yerr)), sd=5.0)
# The parameters of the RotationTerm kernel
logamp = pm.Normal("logamp", mu=np.log(np.var(y)), sd=5.0)
logperiod = pm.Normal("logperiod", mu=np.log(init_period), sd=5.0)
logQ0 = pm.Normal("logQ0", mu=1.0, sd=10.0)
logdeltaQ = pm.Normal("logdeltaQ", mu=2.0, sd=10.0)
mix = pm.Uniform("mix", lower=0, upper=1.0)
# Track the period as a deterministic
period = pm.Deterministic("period", tt.exp(logperiod))
# Set up the Gaussian Process model
kernel = xo.gp.terms.RotationTerm(log_amp=logamp,
period=period,
log_Q0=logQ0,
log_deltaQ=logdeltaQ,
mix=mix)
gp = xo.gp.GP(kernel, x, yerr**2 + tt.exp(logs2), J=4)
# Compute the Gaussian Process likelihood and add it into the
# the PyMC3 model as a "potential"
pm.Potential("loglike", gp.log_likelihood(y - mean))
# Compute the mean model prediction for plotting purposes
if prediction:
pm.Deterministic("pred", gp.predict())
# Optimize to find the maximum a posteriori parameters
self.map_soln = xo.optimize(start=model.test_point)
# print(self.map_soln)
# print(xo.utils.eval_in_model(model.logpt, self.map_soln))
# assert 0
# Sample from the posterior
np.random.seed(42)
sampler = xo.PyMC3Sampler()
with model:
print("sampling...")
sampler.tune(tune=tune,
start=self.map_soln,
step_kwargs=dict(target_accept=0.9),
cores=cores)
trace = sampler.sample(draws=draws, cores=cores)
# Save samples
samples = pm.trace_to_dataframe(trace)
self.samples = samples
self.period_samples = trace["period"]
self.gp_period = np.median(self.period_samples)
lower = np.percentile(self.period_samples, 16)
upper = np.percentile(self.period_samples, 84)
self.errm = self.gp_period - lower
self.errp = upper - self.gp_period
self.logQ = np.median(trace["logQ0"])
upperQ = np.percentile(trace["logQ0"], 84)
lowerQ = np.percentile(trace["logQ0"], 16)
self.Qerrp = upperQ - self.logQ
self.Qerrm = self.logQ - lowerQ
self.trace = trace
return self.gp_period, self.errp, self.errm, self.logQ, self.Qerrp, \
self.Qerrm
rho_save_sky = pm.Deterministic("rhoSaveSky", rho)
theta_save_sky = pm.Deterministic("thetaSaveSky", theta)
rho, theta = orbit.get_relative_angles(t_data, parallax)
rho_save_data = pm.Deterministic("rhoSaveData", rho)
theta_save_data = pm.Deterministic("thetaSaveData", theta)
# save RV plots
t_dense = pm.Deterministic("tDense", xs_phase * P + jd0)
rv1_dense = pm.Deterministic(
"RV1Dense",
conv * orbit.get_star_velocity(t_dense - jd0)[2] + gamma_keck)
rv2_dense = pm.Deterministic(
"RV2Dense",
conv * orbit.get_planet_velocity(t_dense - jd0)[2] + gamma_keck)
with model:
map_sol0 = xo.optimize(vars=[a_ang, phi])
map_sol1 = xo.optimize(map_sol0, vars=[a_ang, phi, omega, Omega])
map_sol2 = xo.optimize(map_sol1,
vars=[a_ang, logP, phi, omega, Omega, incl, e])
map_sol3 = xo.optimize(map_sol2)
# now let's actually explore the posterior for real
sampler = xo.PyMC3Sampler(finish=500, chains=4)
with model:
burnin = sampler.tune(tune=2000, step_kwargs=dict(target_accept=0.9))
trace = sampler.sample(draws=3000)
pm.backends.ndarray.save_trace(trace, directory="current", overwrite=True)
# Compute the model
uvT = tt.reshape(tt.dot(u, vT), (N * K, 1))
f_model = tt.reshape(ts.dot(D, uvT), (M * Kobs, ))
# Track some values for plotting later
pm.Deterministic("f_model", f_model)
# Save our initial guess
f_model_guess = xo.eval_in_model(f_model)
# The likelihood function assuming known Gaussian uncertainty
pm.Normal("obs", mu=f_model, sd=ferr, observed=f)
# Maximum likelihood solution
with model:
map_soln = xo.optimize()
# Plot some stuff
fig, ax = plt.subplots(1)
ax.plot(lam, I0)
ax.plot(lam, map_soln["vT"].reshape(-1), 'o')
fig, ax = plt.subplots(M, figsize=(3, 8), sharex=True, sharey=True)
F = f.reshape(M, Kobs)
F_model = map_soln["f_model"].reshape(M, Kobs)
for m in range(M):
ax[m].plot(lam[Kpad:-Kpad], F[m] / F[m][0])
ax[m].plot(lam[Kpad:-Kpad], F_model[m] / F[m][0])
ax[m].axis('off')
ntheta = 12
def build_model(mask=None, start=None):
''' Build a PYMC3 model
Parameters
----------
mask : np.ndarray
Boolean array to mask cadences. Cadences that are False will be excluded
from the model fit
start : dict
MAP Solution from exoplanet
Returns
-------
model : pymc3.model.Model
A pymc3 model
map_soln : dict
Best fit solution
'''
if mask is None:
mask = np.ones(len(time), dtype=bool)
with pm.Model() as model:
# Parameters for the stellar properties
mean = pm.Normal("mean", mu=0.0, sd=10.0)
u_star = xo.distributions.QuadLimbDark("u_star")
m_star = pm.Normal("m_star", mu=M_star[0], sd=M_star[1])
r_star = pm.Normal("r_star", mu=R_star[0], sd=R_star[1])
t_star = pm.Normal("t_star", mu=T_star[0], sd=T_star[1])
# Prior to require physical parameters
pm.Potential("m_star_prior", tt.switch(m_star > 0, 0, -np.inf))
pm.Potential("r_star_prior", tt.switch(r_star > 0, 0, -np.inf))
# Orbital parameters for the planets
logP = pm.Normal("logP",
mu=np.log(period_value),
sd=0.01,
shape=shape)
t0 = pm.Normal("t0", mu=t0_value, sd=0.01, shape=shape)
b = pm.Uniform("b", lower=0, upper=1, testval=0.5, shape=shape)
logr = pm.Normal("logr",
sd=1.0,
mu=0.5 * np.log(np.array(depth_value)) +
np.log(R_star[0]),
shape=shape)
r_pl = pm.Deterministic("r_pl", tt.exp(logr))
ror = pm.Deterministic("ror", r_pl / r_star)
# Tracking planet parameters
period = pm.Deterministic("period", tt.exp(logP))
# Orbit model
orbit = xo.orbits.KeplerianOrbit(r_star=r_star,
m_star=m_star,
period=period,
t0=t0,
b=b)
incl = pm.Deterministic('incl', orbit.incl)
a = pm.Deterministic('a', orbit.a)
teff = pm.Deterministic('teff', t_star * tt.sqrt(0.5 * (1 / a)))
# Compute the model light curve using starry
light_curves = xo.StarryLightCurve(u_star).get_light_curve(
orbit=orbit, r=r_pl, t=time[mask], texp=texp) * 1e3
light_curve = pm.math.sum(light_curves, axis=-1) + mean
pm.Deterministic("light_curves", light_curves)
# GP
# --------
logs2 = pm.Normal("logs2",
mu=np.log(1e-4 * np.var(raw_flux[mask])),
sd=10)
logsigma = pm.Normal("logsigma",
mu=np.log(np.std(raw_flux[mask])),
sd=10)
logrho = pm.Normal("logrho", mu=np.log(150), sd=10)
kernel = xo.gp.terms.Matern32Term(log_rho=logrho,
log_sigma=logsigma)
gp = xo.gp.GP(kernel, time[mask],
tt.exp(logs2) + raw_flux_err[mask]**2)
# Motion model
#------------------
A = tt.dot(X_pld[mask].T, gp.apply_inverse(X_pld[mask]))
B = tt.dot(X_pld[mask].T, gp.apply_inverse(raw_flux[mask, None]))
C = tt.slinalg.solve(A, B)
motion_model = pm.Deterministic("motion_model",
tt.dot(X_pld[mask], C)[:, 0])
# Likelihood
#------------------
pm.Potential("obs",
gp.log_likelihood(raw_flux[mask] - motion_model))
# gp predicted flux
gp_pred = gp.predict()
pm.Deterministic("gp_pred", gp_pred)
pm.Deterministic("weights", C)
# Optimize
#------------------
if start is None:
start = model.test_point
map_soln = xo.optimize(start=start, vars=[logrho, logsigma])
map_soln = xo.optimize(start=start, vars=[logr])
map_soln = xo.optimize(start=map_soln, vars=[logs2])
map_soln = xo.optimize(start=map_soln,
vars=[logrho, logsigma, logs2, logr])
map_soln = xo.optimize(start=map_soln, vars=[mean, logr])
map_soln = xo.optimize(start=map_soln, vars=[logP, t0])
map_soln = xo.optimize(start=map_soln, vars=[b])
map_soln = xo.optimize(start=map_soln, vars=[u_star])
map_soln = xo.optimize(start=map_soln,
vars=[logrho, logsigma, logs2])
map_soln = xo.optimize(start=map_soln)
return model, map_soln, gp
def build_model(mask=None, start=None):
with pm.Model() as model:
# The baseline flux
mean = pm.Normal("mean", mu=0.0, sd=0.00001)
# The time of a reference transit for each planet
t0 = pm.Normal("t0", mu=t0s, sd=1.0, shape=1)
# The log period; also tracking the period itself
logP = pm.Normal("logP", mu=np.log(periods), sd=0.01, shape=1)
rho_star = pm.Normal("rho_star", mu=0.14, sd=0.01, shape=1)
r_star = pm.Normal("r_star", mu=2.7, sd=0.01, shape=1)
period = pm.Deterministic("period", pm.math.exp(logP))
# The Kipping (2013) parameterization for quadratic limb darkening paramters
u = xo.distributions.QuadLimbDark("u", testval=np.array([0.3, 0.2]))
r = pm.Uniform(
"r", lower=0.01, upper=0.3, shape=1, testval=0.15)
b = xo.distributions.ImpactParameter(
"b", ror=r, shape=1, testval=0.5)
# Transit jitter & GP parameters
logs2 = pm.Normal("logs2", mu=np.log(np.var(y)), sd=10)
logw0 = pm.Normal("logw0", mu=0, sd=10)
logSw4 = pm.Normal("logSw4", mu=np.log(np.var(y)), sd=10)
# Set up a Keplerian orbit for the planets
orbit = xo.orbits.KeplerianOrbit(period=period, t0=t0, b=b, rho_star=rho_star,r_star=r_star)
# Compute the model light curve using starry
light_curves = xo.LimbDarkLightCurve(u).get_light_curve(
orbit=orbit, r=r, t=t
)
light_curve = pm.math.sum(light_curves, axis=-1) + mean
# Here we track the value of the model light curve for plotting
# purposes
pm.Deterministic("light_curves", light_curves)
kernel = xo.gp.terms.SHOTerm(log_Sw4=logSw4, log_w0=logw0, Q=1 / np.sqrt(2))
gp = xo.gp.GP(kernel, t, tt.exp(logs2) + tt.zeros(len(t)), mean=light_curve)
gp.marginal("gp", observed=y)
pm.Deterministic("gp_pred", gp.predict())
# The likelihood function assuming known Gaussian uncertainty
pm.Normal("obs", mu=light_curve, sd=yerr, observed=y)
# Fit for the maximum a posteriori parameters given the simuated
# dataset
map_soln = xo.optimize(start=model.test_point)
return model, map_soln
model, map_soln = build_model()
gp_mod = map_soln["gp_pred"] + map_soln["mean"]
plt.clf()
plt.plot(t, y, ".k", ms=4, label="data")
plt.plot(t, gp_mod, lw=1,label="gp model")
plt.plot(t, map_soln["light_curves"], lw=1,label="transit model")
plt.xlim(t.min(), t.max())
plt.ylabel("relative flux")
plt.xlabel("time [days]")
plt.legend(fontsize=10)
_ = plt.title("map model")
np.random.seed(42)
with model:
trace = pm.sample(
tune=3000,
draws=3000,
start=map_soln,
cores=2,
chains=2,
step=xo.get_dense_nuts_step(target_accept=0.9),
)
pm.summary(trace, varnames=["period", "t0", "r", "b", "u", "mean", "rho_star","logw0","logSw4","logs2"])
import corner
samples = pm.trace_to_dataframe(trace, varnames=["period", "r"])
truth = np.concatenate(
xo.eval_in_model([period, r], model.test_point, model=model)
)
_ = corner.corner(
samples,
truths=truth,
labels=["period 1", "radius 1"],
)
# Compute the GP prediction
gp_mod = np.median(trace["gp_pred"] + trace["mean"][:, None], axis=0)
# Get the posterior median orbital parameters
p = np.median(trace["period"])
t0 = np.median(trace["t0"])
# Plot the folded data
x_fold = (t - t0 + 0.5 * p) % p - 0.5 * p
plt.plot(x_fold, y - gp_mod, ".k", label="data", zorder=-1000)
# Overplot the phase binned light curve
bins = np.linspace(-0.41, 0.41, 50)
denom, _ = np.histogram(x_fold, bins)
num, _ = np.histogram(x_fold, bins, weights=y)
denom[num == 0] = 1.0
plt.plot(0.5 * (bins[1:] + bins[:-1]), num / denom, "o", color="C2", label="binned")
# Plot the folded model
inds = np.argsort(x_fold)
inds = inds[np.abs(x_fold)[inds] < 0.3]
pred = trace["light_curves"][:, inds, 0]
pred = np.percentile(pred, [16, 50, 84], axis=0)
plt.plot(x_fold[inds], pred[1], color="C1", label="model")
art = plt.fill_between(
x_fold[inds], pred[0], pred[2], color="C1", alpha=0.5, zorder=1000
)
art.set_edgecolor("none")
# Annotate the plot with the planet's period
txt = "period = {0:.5f} +/- {1:.5f} d".format(
np.mean(trace["period"]), np.std(trace["period"])
)
plt.annotate(
txt,
(0, 0),
xycoords="axes fraction",
xytext=(5, 5),
textcoords="offset points",
ha="left",
va="bottom",
fontsize=12,
)
plt.legend(fontsize=10, loc=4)
plt.xlim(-0.5 * p, 0.5 * p)
plt.xlabel("time since transit [days]")
plt.ylabel("de-trended flux")
plt.xlim(-0.3, 0.3);
# calculate light curves
light_curves[j] = exoSLC.get_light_curve(orbit=orbit, r=rp[npl], t=t_[m_], oversample=oversample)
summed_light_curve[j] = pm.math.sum(light_curves[j], axis=-1) + flux0[j]*T.ones(len(t_[m_]))
model_flux[j] = pm.Deterministic('model_flux_{0}'.format(j), summed_light_curve[j])
# here's the GP (w/ kernel by season)
gp[j] = exo.gp.GP(kernel[q%4], t_[m_], T.exp(logvar[j])*T.ones(len(t_[m_])))
# add custom potential (log-prob fxn) with the GP likelihood
pm.Potential('obs_{0}'.format(j), gp[j].log_likelihood(f_[m_] - model_flux[j]))
with hbm_model:
hbm_map = exo.optimize(start=hbm_model.test_point, vars=[flux0, logvar])
if local_trend_type[npl][ng-1] == "linear":
hbm_map = exo.optimize(start=hbm_map, vars=[C0, C1])
if local_trend_type[npl][ng-1] == "quadratic":
hbm_map = exo.optimize(start=hbm_map, vars=[C0, C1, C2])
if local_trend_type[npl][ng-1] == "sinusoid":
hbm_map = exo.optimize(start=hbm_map, vars=[C0, C1, A, B])
# sample from the posterior
with hbm_model:
hbm_trace = pm.sample(tune=3000, draws=1000, start=hbm_map, chains=2,
step=exo.get_dense_nuts_step(target_accept=0.9))
# save the results
def _optimize(self, start=None, verbose=True):
with self._model as model:
if start is None:
start = model.test_point
map_soln = xo.optimize(start=start, vars=[model.mean], verbose=verbose)
map_soln = xo.optimize(start=start, vars=[model.logrho, model.logsigma, model.mean], verbose=verbose)
map_soln = xo.optimize(start=start, vars=[model.logrho, model.logsigma, model.logs2], verbose=verbose)
map_soln = xo.optimize(start=map_soln, vars=[model.logP, model.rprs, model.t0], verbose=verbose)
map_soln = xo.optimize(start=map_soln, vars=[model.u], verbose=verbose)
map_soln = xo.optimize(start=map_soln, vars=[model.ep, model.dp], verbose=verbose)
map_soln = xo.optimize(start=map_soln, vars=[model.inclination], verbose=verbose)
map_soln = xo.optimize(start=map_soln, vars=[model.albedo], verbose=verbose)
map_soln = xo.optimize(start=map_soln, vars=[model.albedo, model.dT, model.phase_shift], verbose=verbose)
map_soln = xo.optimize(start=map_soln, vars=[model.logP, model.rprs, model.t0, model.u], verbose=verbose)
map_soln = xo.optimize(start=start, vars=[model.logrho, model.logsigma, model.logs2], verbose=verbose)
map_soln = xo.optimize(start=map_soln, vars=[model.albedo, model.dT], verbose=verbose)
map_soln = xo.optimize(start=map_soln, vars=[model.ep, model.dp], verbose=verbose)
map_soln = xo.optimize(start=map_soln, vars=[model.albedo, model.inclination, model.t0,
model.logP, model.u, model.ep, model.dp], verbose=verbose)
map_soln = xo.optimize(start=map_soln, vars=[model.ep, model.dp, model.phase_shift, model.dT,
model.albedo, model.inclination, model.t0, model.logP, model.rprs, model.logrho, model.logsigma, model.logs2, model.mean, model.u], verbose=verbose)
return map_soln
def build_model(mask=None, start=None):
with pm.Model() as model:
# The baseline flux
mean = pm.Normal("mean", mu=0.0, sd=0.00001)
# The time of a reference transit for each planet
t0 = pm.Normal("t0", mu=t0s, sd=1.0, shape=1)
# The log period; also tracking the period itself
logP = pm.Normal("logP", mu=np.log(periods), sd=0.01, shape=1)
rho_star = pm.Normal("rho_star", mu=0.14, sd=0.01, shape=1)
r_star = pm.Normal("r_star", mu=2.7, sd=0.01, shape=1)
period = pm.Deterministic("period", pm.math.exp(logP))
# The Kipping (2013) parameterization for quadratic limb darkening paramters
u = xo.distributions.QuadLimbDark("u", testval=np.array([0.3, 0.2]))
r = pm.Uniform("r", lower=0.01, upper=0.3, shape=1, testval=0.15)
b = xo.distributions.ImpactParameter("b", ror=r, shape=1, testval=0.5)
# Transit jitter & GP parameters
logs2 = pm.Normal("logs2", mu=np.log(np.var(y)), sd=10)
logw0 = pm.Normal("logw0", mu=0, sd=10)
logSw4 = pm.Normal("logSw4", mu=np.log(np.var(y)), sd=10)
# Set up a Keplerian orbit for the planets
orbit = xo.orbits.KeplerianOrbit(period=period,
t0=t0,
b=b,
rho_star=rho_star,
r_star=r_star)
# Compute the model light curve using starry
light_curves = xo.LimbDarkLightCurve(u).get_light_curve(orbit=orbit,
r=r,
t=t)
light_curve = pm.math.sum(light_curves, axis=-1) + mean
# Here we track the value of the model light curve for plotting
# purposes
pm.Deterministic("light_curves", light_curves)
S1 = pm.InverseGamma(
"S1", **estimate_inverse_gamma_parameters(0.5**2, 10.0**2))
S2 = pm.InverseGamma(
"S2", **estimate_inverse_gamma_parameters(0.25**2, 1.0**2))
w1 = pm.InverseGamma(
"w1", **estimate_inverse_gamma_parameters(2 * np.pi / 10.0, np.pi))
w2 = pm.InverseGamma(
"w2", **estimate_inverse_gamma_parameters(0.5 * np.pi, 2 * np.pi))
log_Q = pm.Uniform("log_Q", lower=np.log(2), upper=np.log(10))
# Set up the kernel an GP
kernel = terms.SHOTerm(S_tot=S1, w0=w1, Q=1.0 / np.sqrt(2))
kernel += terms.SHOTerm(S_tot=S2, w0=w2, log_Q=log_Q)
gp = GP(kernel, t, yerr**2, mean=mean)
gp.marginal("gp", observed=y)
pm.Deterministic("gp_pred", gp.predict())
# The likelihood function assuming known Gaussian uncertainty
pm.Normal("obs", mu=light_curve, sd=yerr, observed=y)
# Fit for the maximum a posteriori parameters given the simuated
# dataset
map_soln = xo.optimize(start=model.test_point)
return model, map_soln
"w1", **estimate_inverse_gamma_parameters(2 * np.pi / 10.0, np.pi))
w2 = pm.InverseGamma(
"w2", **estimate_inverse_gamma_parameters(0.5 * np.pi, 2 * np.pi))
log_Q = pm.Uniform("log_Q", lower=np.log(2), upper=np.log(10))
# Set up the kernel an GP
kernel = terms.SHOTerm(S_tot=S1, w0=w1, Q=1.0 / np.sqrt(2))
kernel += terms.SHOTerm(S_tot=S2, w0=w2, log_Q=log_Q)
gp = GP(kernel, t, yerr**2, mean=mean)
# Condition the GP on the observations and add the marginal likelihood
# to the model
gp.marginal("gp", observed=y)
with model:
map_soln = xo.optimize(start=model.test_point)
with model:
mu, var = xo.eval_in_model(
gp.predict(true_t, return_var=True, predict_mean=True), map_soln)
# Plot the prediction and the 1-sigma uncertainty
plt.errorbar(t, y, yerr=yerr, fmt=".k", capsize=0, label="data")
plt.plot(true_t, true_y, "k", lw=1.5, alpha=0.3, label="truth")
sd = np.sqrt(var)
art = plt.fill_between(true_t, mu + sd, mu - sd, color="C1", alpha=0.3)
art.set_edgecolor("none")
plt.plot(true_t, mu, color="C1", label="prediction")
plt.legend(fontsize=12)
def build_model(mask):
with pm.Model() as model:
# Systemic parameters
mean_lc = pm.Normal("mean_lc", mu=0.0, sd=5.0)
mean_rv = pm.Normal("mean_rv", mu=0.0, sd=50.0)
u1 = xo.QuadLimbDark("u1")
u2 = xo.QuadLimbDark("u2")
# Parameters describing the primary
M1 = pm.Lognormal("M1", mu=0.0, sigma=10.0, testval=0.696)
R1 = pm.Lognormal("R1", mu=0.0, sigma=10.0, testval=0.687)
# Secondary ratios
k = pm.Lognormal("k", mu=0.0, sigma=10.0,
testval=0.9403) # radius ratio
q = pm.Lognormal("q", mu=0.0, sigma=10.0, testval=0.9815) # mass ratio
s = pm.Lognormal("s", mu=np.log(0.5),
sigma=10.0) # surface brightness ratio
# Prior on flux ratio
pm.Normal(
"flux_prior",
mu=lit_flux_ratio[0],
sigma=lit_flux_ratio[1],
observed=k**2 * s,
)
# Parameters describing the orbit
b = xo.ImpactParameter("b", ror=k, testval=1.5)
period = pm.Lognormal("period", mu=np.log(lit_period), sigma=1.0)
t0 = pm.Normal("t0", mu=lit_t0, sigma=1.0)
# Parameters describing the eccentricity: ecs = [e * cos(w), e * sin(w)]
ecs = xo.UnitDisk("ecs", testval=np.array([1e-5, 0.0]))
ecc = pm.Deterministic("ecc", tt.sqrt(tt.sum(ecs**2)))
omega = pm.Deterministic("omega", tt.arctan2(ecs[1], ecs[0]))
# Build the orbit
R2 = pm.Deterministic("R2", k * R1)
M2 = pm.Deterministic("M2", q * M1)
orbit = xo.orbits.KeplerianOrbit(
period=period,
t0=t0,
ecc=ecc,
omega=omega,
b=b,
r_star=R1,
m_star=M1,
m_planet=M2,
)
# Track some other orbital elements
pm.Deterministic("incl", orbit.incl)
pm.Deterministic("a", orbit.a)
# Noise model for the light curve
sigma_lc = pm.InverseGamma("sigma_lc",
testval=1.0,
**xo.estimate_inverse_gamma_parameters(
0.1, 2.0))
S_tot_lc = pm.InverseGamma("S_tot_lc",
testval=2.5,
**xo.estimate_inverse_gamma_parameters(
1.0, 5.0))
ell_lc = pm.InverseGamma("ell_lc",
testval=2.0,
**xo.estimate_inverse_gamma_parameters(
1.0, 5.0))
kernel_lc = xo.gp.terms.SHOTerm(S_tot=S_tot_lc,
w0=2 * np.pi / ell_lc,
Q=1.0 / 3)
# Noise model for the radial velocities
sigma_rv1 = pm.InverseGamma("sigma_rv1",
testval=1.0,
**xo.estimate_inverse_gamma_parameters(
0.5, 5.0))
sigma_rv2 = pm.InverseGamma("sigma_rv2",
testval=1.0,
**xo.estimate_inverse_gamma_parameters(
0.5, 5.0))
S_tot_rv = pm.InverseGamma("S_tot_rv",
testval=2.5,
**xo.estimate_inverse_gamma_parameters(
1.0, 5.0))
ell_rv = pm.InverseGamma("ell_rv",
testval=2.0,
**xo.estimate_inverse_gamma_parameters(
1.0, 5.0))
kernel_rv = xo.gp.terms.SHOTerm(S_tot=S_tot_rv,
w0=2 * np.pi / ell_rv,
Q=1.0 / 3)
# Set up the light curve model
lc = xo.SecondaryEclipseLightCurve(u1, u2, s)
def model_lc(t):
return (
mean_lc + 1e3 *
lc.get_light_curve(orbit=orbit, r=R2, t=t, texp=texp)[:, 0])
# Condition the light curve model on the data
gp_lc = xo.gp.GP(kernel_lc,
x[mask],
tt.zeros(mask.sum())**2 + sigma_lc**2,
mean=model_lc)
gp_lc.marginal("obs_lc", observed=y[mask])
# Set up the radial velocity model
def model_rv1(t):
return mean_rv + 1e-3 * orbit.get_radial_velocity(t)
def model_rv2(t):
return mean_rv - 1e-3 * orbit.get_radial_velocity(t) / q
# Condition the radial velocity model on the data
gp_rv1 = xo.gp.GP(kernel_rv,
x_rv,
tt.zeros(len(x_rv))**2 + sigma_rv1**2,
mean=model_rv1)
gp_rv1.marginal("obs_rv1", observed=y1_rv)
gp_rv2 = xo.gp.GP(kernel_rv,
x_rv,
tt.zeros(len(x_rv))**2 + sigma_rv2**2,
mean=model_rv2)
gp_rv2.marginal("obs_rv2", observed=y2_rv)
# Optimize the logp
map_soln = model.test_point
# First the RV parameters
map_soln = xo.optimize(map_soln, [mean_rv, q])
map_soln = xo.optimize(
map_soln, [mean_rv, sigma_rv1, sigma_rv2, S_tot_rv, ell_rv])
# Then the LC parameters
map_soln = xo.optimize(map_soln, [mean_lc, R1, k, s, b])
map_soln = xo.optimize(map_soln, [mean_lc, R1, k, s, b, u1, u2])
map_soln = xo.optimize(map_soln, [mean_lc, sigma_lc, S_tot_lc, ell_lc])
map_soln = xo.optimize(map_soln, [t0, period])
# Then all the parameters together
map_soln = xo.optimize(map_soln)
model.gp_lc = gp_lc
model.model_lc = model_lc
model.gp_rv1 = gp_rv1
model.model_rv1 = model_rv1
model.gp_rv2 = gp_rv2
model.model_rv2 = model_rv2
model.x = x[mask]
model.y = y[mask]
return model, map_soln
def build_model(mask=None):
if mask is None:
mask = np.ones_like(x, dtype=bool)
with pm.Model() as model:
# Stellar parameters
mean = pm.Normal("mean", mu=0.0, sigma=10.0)
u = xo.distributions.QuadLimbDark("u")
# Gaussian process noise model
sigma = pm.InverseGamma("sigma", alpha=3.0, beta=2 * np.median(yerr))
S_tot = pm.InverseGamma("S_tot", alpha=3.0, beta=2 * np.median(yerr))
ell = pm.Lognormal("ell", mu=0.0, sigma=1.0)
Q = 1.0 / 3.0
w0 = 2 * np.pi / ell
S0 = S_tot / (w0 * Q)
kernel = xo.gp.terms.SHOTerm(S0=S0, w0=w0, Q=Q)
# Transit parameters
t0 = pm.Bound(
pm.Normal,
lower=t0_guess - max_duration,
upper=t0_guess + max_duration,
)(
"t0",
mu=t0_guess,
sigma=0.5 * duration_guess,
testval=t0_guess,
shape=num_toi,
)
depth = pm.Lognormal(
"transit_depth",
mu=np.log(depth_guess),
sigma=np.log(1.2),
shape=num_toi,
)
duration = pm.Bound(pm.Lognormal,
lower=min_duration,
upper=max_duration)(
"transit_duration",
mu=np.log(duration_guess),
sigma=np.log(1.2),
shape=num_toi,
testval=min(
max(duration_guess, 2 * min_duration),
0.99 * max_duration),
)
b = xo.distributions.UnitUniform("b", shape=num_toi)
# Dealing with period, treating single transits properly
period_params = []
period_values = []
t_max_values = []
for n in range(num_toi):
if single_transit[n]:
period = pm.Pareto(
f"period_{n}",
m=period_min[n],
alpha=2.0 / 3,
testval=period_guess[n],
)
period_params.append(period)
t_max_values.append(t0[n])
else:
t_max = pm.Bound(
pm.Normal,
lower=t_max_guess[n] - max_duration[n],
upper=t_max_guess[n] + max_duration[n],
)(
f"t_max_{n}",
mu=t_max_guess[n],
sigma=0.5 * duration_guess[n],
testval=t_max_guess[n],
)
period = (t_max - t0[n]) / num_periods[n]
period_params.append(t_max)
t_max_values.append(t_max)
period_values.append(period)
period = pm.Deterministic("period", tt.stack(period_values))
t_max = pm.Deterministic("t_max", tt.stack(t_max_values))
# Compute the radius ratio from the transit depth, impact parameter, and
# limb darkening parameters making the small-planet assumption
u1 = u[0]
u2 = u[1]
mu = tt.sqrt(1 - b**2)
ror = pm.Deterministic(
"ror",
tt.sqrt(1e-3 * depth * (1 - u1 / 3 - u2 / 6) /
(1 - u1 * (1 - mu) - u2 * (1 - mu)**2)),
)
# Set up the orbit
orbit = xo.orbits.KeplerianOrbit(period=period,
duration=duration,
t0=t0,
b=b)
# We're going to track the implied density for reasons that will become clear later
pm.Deterministic("rho_circ", orbit.rho_star)
# Set up the mean transit model
star = xo.LimbDarkLightCurve(u)
lc_model = tess_world.LightCurveModels(mean, star, orbit, ror)
# Finally the GP observation model
gp = xo.gp.GP(kernel, x[mask], yerr[mask]**2 + sigma**2, mean=lc_model)
gp.marginal("obs", observed=y[mask])
# This is a check on the transit depth constraint
D = tt.concatenate(
(
lc_model.light_curves(x[mask]) / depth[None, :],
tt.ones((mask.sum(), 1)),
),
axis=-1,
)
DTD = tt.dot(D.T, gp.apply_inverse(D))
DTy = tt.dot(D.T, gp.apply_inverse(y[mask, None]))
model.w = tt.slinalg.solve(DTD, DTy)[:, 0]
model.sigma_w = tt.sqrt(
tt.diag(tt.slinalg.solve(DTD, tt.eye(num_toi + 1))))
# Double check that everything looks good - we shouldn't see any NaNs!
print(model.check_test_point())
# Optimize the model
map_soln = model.test_point
map_soln = xo.optimize(map_soln, [sigma])
map_soln = xo.optimize(map_soln, [mean, depth, b, duration])
map_soln = xo.optimize(map_soln, [sigma, S_tot, ell])
map_soln = xo.optimize(map_soln, [mean, u])
map_soln = xo.optimize(map_soln, period_params)
map_soln = xo.optimize(map_soln)
# Save some of the key parameters
model.map_soln = map_soln
model.lc_model = lc_model
model.gp = gp
model.mask = mask
model.x = x[mask]
model.y = y[mask]
model.yerr = yerr[mask]
return model
def flatten_with_gp(lc,
break_tolerance,
min_period,
bin_factor=None,
return_trend=False):
"""
Detrend the flux from an alderaan LiteCurve using a celerite RotationTerm GP kernel
The mean function of each uninterrupted segment of flux is modeled as an exponential
Fmean = F0*(1+A*exp(-t/tau))
Parameters
----------
lc : alderaan.LiteCurve
must have .time, .flux and .mask attributes
break_tolerance : int
number of cadences considered a large gap in time
min_period : float
lower bound on primary period for RotationTerm kernel
return_trend : bool (default=False)
if True, return the trend inferred from the GP fit
Returns
-------
lc : alderaan.LiteCurve
LiteCurve with trend removed from lc.flux
gp_trend : ndarray
trend inferred from GP fit (only returned if return_trend == True)
"""
# find gaps/breaks/jumps in the data
gaps = identify_gaps(lc, break_tolerance=break_tolerance)
gaps[-1] -= 1
# initialize data arrays and lists of segments
gp_time = np.array(lc.time, dtype="float64")
gp_flux = np.array(lc.flux, dtype="float64")
gp_mask = np.sum(lc.mask, 0) == 0
time_segs = []
flux_segs = []
mask_segs = []
for i in range(len(gaps) - 1):
time_segs.append(gp_time[gaps[i]:gaps[i + 1]])
flux_segs.append(gp_flux[gaps[i]:gaps[i + 1]])
mask_segs.append(gp_mask[gaps[i]:gaps[i + 1]])
mean_flux = []
approx_var = []
for i in range(len(gaps) - 1):
m = mask_segs[i]
mean_flux.append(np.mean(flux_segs[i][m]))
approx_var.append(np.var(flux_segs[i] - sig.medfilt(flux_segs[i], 13)))
# put segments into groups of ten
nseg = len(time_segs)
ngroup = int(np.ceil(nseg / 10))
seg_groups = np.array(np.arange(ngroup + 1) * np.ceil(nseg / ngroup),
dtype="int")
seg_groups[-1] = len(gaps) - 1
# identify rotation period to initialize GP
ls_estimate = exo.estimators.lomb_scargle_estimator(gp_time, gp_flux, max_peaks=1, \
min_period=min_period, max_period=91.0, \
samples_per_peak=50)
peak_per = ls_estimate["peaks"][0]["period"]
# set up lists to hold trend info
trend_maps = [None] * ngroup
# optimize the GP for each group of segments
for j in range(ngroup):
sg0 = seg_groups[j]
sg1 = seg_groups[j + 1]
nuse = sg1 - sg0
with pm.Model() as trend_model:
log_amp = pm.Normal("log_amp", mu=np.log(np.std(gp_flux)), sd=5)
log_per_off = pm.Normal("log_per_off",
mu=0,
sd=5,
testval=np.log(peak_per - min_period))
log_Q0_off = pm.Normal("log_Q0_off", mu=0, sd=10)
log_deltaQ = pm.Normal("log_deltaQ", mu=2, sd=10)
mix = pm.Uniform("mix", lower=0, upper=1)
P = pm.Deterministic("P", min_period + T.exp(log_per_off))
Q0 = pm.Deterministic("Q0", 1 / T.sqrt(2) + T.exp(log_Q0_off))
kernel = exo.gp.terms.RotationTerm(log_amp=log_amp,
period=P,
Q0=Q0,
log_deltaQ=log_deltaQ,
mix=mix)
# exponential trend
logtau = pm.Normal("logtau",
mu=np.log(3) * np.ones(nuse),
sd=5 * np.ones(nuse),
shape=nuse)
exp_amp = pm.Normal('exp_amp',
mu=np.zeros(nuse),
sd=np.std(gp_flux) * np.ones(nuse),
shape=nuse)
# nuissance parameters per segment
flux0 = pm.Normal('flux0',
mu=np.array(mean_flux[sg0:sg1]),
sd=np.std(gp_flux) * np.ones(nuse),
shape=nuse)
logvar = pm.Normal('logvar',
mu=np.log(approx_var[sg0:sg1]),
sd=10 * np.ones(nuse),
shape=nuse)
# now set up the GP
gp = [None] * nuse
gp_pred = [None] * nuse
for i in range(nuse):
m = mask_segs[sg0 + i]
t = time_segs[sg0 + i][m] - time_segs[sg0 + i][m][0]
ramp = 1 + exp_amp[i] * np.exp(-t / np.exp(logtau[i]))
gp[i] = exo.gp.GP(
kernel, time_segs[sg0 + i][m],
T.exp(logvar[i]) * T.ones(len(time_segs[sg0 + i][m])))
pm.Potential(
'obs_{0}'.format(i),
gp[i].log_likelihood(flux_segs[sg0 + i][m] -
flux0[i] * ramp))
with trend_model:
trend_maps[j] = exo.optimize(start=trend_model.test_point)
# set up mean and variance vectors
gp_mean = np.ones_like(gp_flux)
gp_var = np.ones_like(gp_flux)
for i in range(nseg):
j = np.argmin(seg_groups <= i) - 1
g0 = gaps[i]
g1 = gaps[i + 1]
F0_ = trend_maps[j]["flux0"][i - seg_groups[j]]
A_ = trend_maps[j]["exp_amp"][i - seg_groups[j]]
tau_ = np.exp(trend_maps[j]["logtau"][i - seg_groups[j]])
t_ = gp_time[g0:g1] - gp_time[g0]
gp_mean[g0:g1] = F0_ * (1 + A_ * np.exp(-t_ / tau_))
gp_var[g0:g1] = np.ones(g1 - g0) * np.exp(
trend_maps[j]["logvar"][i - seg_groups[j]])
# increase variance for cadences in transit (yes, this is hacky, but it works)
# using gp.predict() inside the initial model was crashing jupyter, making debugging slow
gp_var[~gp_mask] *= 1e12
# now evaluate the GP to get the final trend
gp_trend = np.zeros_like(gp_flux)
for j in range(ngroup):
start = gaps[seg_groups[j]]
end = gaps[seg_groups[j + 1]]
m = gp_mask[start:end]
with pm.Model() as trend_model:
log_amp = trend_maps[j]["log_amp"]
P = trend_maps[j]["P"]
Q0 = trend_maps[j]["Q0"]
log_deltaQ = trend_maps[j]["log_deltaQ"]
mix = trend_maps[j]["mix"]
kernel = exo.gp.terms.RotationTerm(log_amp=log_amp,
period=P,
Q0=Q0,
log_deltaQ=log_deltaQ,
mix=mix)
gp = exo.gp.GP(kernel, gp_time[start:end], gp_var[start:end])
gp.log_likelihood(gp_flux[start:end] - gp_mean[start:end])
gp_trend[start:end] = gp.predict().eval() + gp_mean[start:end]
# now remove the trend
lc.flux = lc.flux - gp_trend + 1.0
# return results
if return_trend:
return lc, gp_trend
else:
return lc
