def cov(self, x1, x2=None):
if x2 is None:
xx = self.metric.gram(x1, x1)
debug(tt.arcsin(2*xx/((1 + 2*xx)**2)), 'xx')
return self.var * tt.arcsin(2*xx/((1 + 2*xx)**2))
else:
return self.var * tt.arcsin(2*self.metric.gram(x1, x2)/((1 + 2*self.metric.gram(x1, x1))*(1 + 2*self.metric.gram(x2, x2))))
def get_stencil(self, t, r=None, texp=None):
if r is None or texp is None:
return tt.shape_padright(t)
z = tt.zeros_like(self.a)
r = tt.as_tensor_variable(r)
R = self.r_star + z
hp = 0.5 * self.period
if self.ecc is None:
# Equation 14 from Winn (2010)
k = r / self.r_star
arg1 = tt.square(1 + k) - tt.square(self.b)
arg2 = tt.square(1 - k) - tt.square(self.b)
factor = R / (self.a * self.sin_incl)
hdur1 = hp * tt.arcsin(factor * tt.sqrt(arg1)) / np.pi
hdur2 = hp * tt.arcsin(factor * tt.sqrt(arg2)) / np.pi
ts = [-hdur1, -hdur2, hdur2, hdur1]
flag = z
else:
M_contact1 = self.contact_points_op(self.a, self.ecc,
self.cos_omega, self.sin_omega,
self.cos_incl + z,
self.sin_incl + z, R + r)
M_contact2 = self.contact_points_op(self.a, self.ecc,
self.cos_omega, self.sin_omega,
self.cos_incl + z,
self.sin_incl + z, R - r)
flag = M_contact1[2] + M_contact2[2]
ts = [
tt.mod(
(M_contact1[0] - self.M0) / self.n + hp, self.period) - hp,
tt.mod(
(M_contact2[0] - self.M0) / self.n + hp, self.period) - hp,
tt.mod(
(M_contact2[1] - self.M0) / self.n + hp, self.period) - hp,
tt.mod(
(M_contact1[1] - self.M0) / self.n + hp, self.period) - hp
]
start = self.period * tt.floor((tt.min(t) - self.t0) / self.period)
end = self.period * (tt.ceil((tt.max(t) - self.t0) / self.period) + 1)
start += self.t0
end += self.t0
tout = []
for i in range(4):
if z.ndim < 1:
tout.append(ts[i] + tt.arange(start, end, self.period))
else:
tout.append(
theano.scan(
fn=lambda t0, s0, e0, p0: t0 + tt.arange(s0, e0, p0),
sequences=[ts[i], start, end, self.period],
)[0].flatten())
ts = tt.sort(tt.concatenate(tout))
return ts, flag
def get_stencil(self, t, r=None, texp=None):
if r is None or texp is None:
return tt.shape_padright(t)
z = tt.zeros_like(self.a)
r = tt.as_tensor_variable(r)
R = self.r_star + z
hp = 0.5 * self.period
if self.ecc is None:
# Equation 14 from Winn (2010)
k = r / self.r_star
arg1 = tt.square(1 + k) - tt.square(self.b)
arg2 = tt.square(1 - k) - tt.square(self.b)
factor = R / (self.a * self.sin_incl)
hdur1 = hp * tt.arcsin(factor * tt.sqrt(arg1)) / np.pi
hdur2 = hp * tt.arcsin(factor * tt.sqrt(arg2)) / np.pi
ts = [-hdur1, -hdur2, hdur2, hdur1]
flag = z
else:
M_contact1 = self.contact_points_op(
self.a, self.ecc, self.cos_omega, self.sin_omega,
self.cos_incl + z, self.sin_incl + z, R + r)
M_contact2 = self.contact_points_op(
self.a, self.ecc, self.cos_omega, self.sin_omega,
self.cos_incl + z, self.sin_incl + z, R - r)
flag = M_contact1[2] + M_contact2[2]
ts = [
tt.mod((M_contact1[0]-self.M0)/self.n+hp, self.period)-hp,
tt.mod((M_contact2[0]-self.M0)/self.n+hp, self.period)-hp,
tt.mod((M_contact2[1]-self.M0)/self.n+hp, self.period)-hp,
tt.mod((M_contact1[1]-self.M0)/self.n+hp, self.period)-hp
]
start = self.period * tt.floor((tt.min(t) - self.t0) / self.period)
end = self.period * (tt.ceil((tt.max(t) - self.t0) / self.period) + 1)
start += self.t0
end += self.t0
tout = []
for i in range(4):
if z.ndim < 1:
tout.append(ts[i] + tt.arange(start, end, self.period))
else:
tout.append(theano.scan(
fn=lambda t0, s0, e0, p0: t0 + tt.arange(s0, e0, p0),
sequences=[ts[i], start, end, self.period],
)[0].flatten())
ts = tt.sort(tt.concatenate(tout))
return ts, flag
def in_transit(self, t, r=0.0, texp=None):
"""Get a list of timestamps that are in transit
Args:
t (vector): A vector of timestamps to be evaluated.
r (Optional): The radii of the planets.
texp (Optional[float]): The exposure time.
Returns:
The indices of the timestamps that are in transit.
"""
z = tt.zeros_like(self.a)
r = tt.as_tensor_variable(r) + z
R = self.r_star + z
# Wrap the times into time since transit
hp = 0.5 * self.period
dt = tt.mod(self._warp_times(t) + hp, self.period) - hp
if self.ecc is None:
# Equation 14 from Winn (2010)
k = r / R
arg = tt.square(1 + k) - tt.square(self.b)
factor = R / (self.a * self.sin_incl)
hdur = hp * tt.arcsin(factor * tt.sqrt(arg)) / np.pi
t_start = -hdur
t_end = hdur
flag = z
else:
M_contact = self.contact_points_op(
self.a,
self.ecc,
self.cos_omega,
self.sin_omega,
self.cos_incl + z,
self.sin_incl + z,
R + r,
)
flag = M_contact[2]
t_start = (M_contact[0] - self.M0) / self.n
t_start = tt.mod(t_start + hp, self.period) - hp
t_end = (M_contact[1] - self.M0) / self.n
t_end = tt.mod(t_end + hp, self.period) - hp
t_start = tt.switch(tt.gt(t_start, 0.0), t_start - self.period,
t_start)
t_end = tt.switch(tt.lt(t_end, 0.0), t_end + self.period, t_end)
if texp is not None:
t_start -= 0.5 * texp
t_end += 0.5 * texp
mask = tt.any(tt.and_(dt >= t_start, dt <= t_end), axis=-1)
result = ifelse(tt.all(tt.eq(flag, 0)),
tt.arange(t.size)[mask], tt.arange(t.size))
return result
def in_transit(self, t, r=0.0, texp=None):
"""Get a list of timestamps that are in transit
Args:
t (vector): A vector of timestamps to be evaluated.
r (Optional): The radii of the planets.
texp (Optional[float]): The exposure time.
Returns:
The indices of the timestamps that are in transit.
"""
z = tt.zeros_like(self.a)
r = tt.as_tensor_variable(r) + z
R = self.r_star + z
# Wrap the times into time since transit
hp = 0.5 * self.period
dt = tt.mod(self._warp_times(t) - self.t0 + hp, self.period) - hp
if self.ecc is None:
# Equation 14 from Winn (2010)
k = r / R
arg = tt.square(1 + k) - tt.square(self.b)
factor = R / (self.a * self.sin_incl)
hdur = hp * tt.arcsin(factor * tt.sqrt(arg)) / np.pi
t_start = -hdur
t_end = hdur
flag = z
else:
M_contact = self.contact_points_op(
self.a, self.ecc, self.cos_omega, self.sin_omega,
self.cos_incl + z, self.sin_incl + z, R + r)
flag = M_contact[2]
t_start = (M_contact[0] - self.M0) / self.n
t_start = tt.mod(t_start + hp, self.period) - hp
t_end = (M_contact[1] - self.M0) / self.n
t_end = tt.mod(t_end + hp, self.period) - hp
t_start = tt.switch(tt.gt(t_start, 0.0),
t_start - self.period, t_start)
t_end = tt.switch(tt.lt(t_end, 0.0),
t_end + self.period, t_end)
if texp is not None:
t_start -= 0.5*texp
t_end += 0.5*texp
mask = tt.any(tt.and_(dt >= t_start, dt <= t_end), axis=-1)
result = ifelse(tt.all(tt.eq(flag, 0)),
tt.arange(t.size)[mask],
tt.arange(t.size))
return result
def th_haversine():
"""Returns a reference to the compiled Haversine distance function"""
from theano import tensor as T
from theano import function
from .vectorops import floatX
coords1 = T.matrix("Coords1", dtype=floatX)
coords2 = T.matrix("Coords2", dtype=floatX)
R = np.array([6367], dtype="int32") # Approximate radius of Mother Earth in kms
coords1 = T.deg2rad(coords1)
coords2 = T.deg2rad(coords2)
lon1, lat1 = coords1[:, 0], coords1[:, 1]
lon2, lat2 = coords2[:, 0], coords2[:, 1]
dlon = lon1 - lon2
dlat = lat1 - lat2
d = T.sin(dlat / 2) ** 2 + T.cos(lat1) * T.cos(lat2) * T.sin(dlon / 2) ** 2
e = 2 * T.arcsin(T.sqrt(d))
d_haversine = e * R
f_ = function([coords1, coords2], outputs=d_haversine)
return f_
def __call__(self, x1, x2):
return self.var * tt.arcsin(2*self.metric(x1, x2)/((1 + 2*self.metric(x1, x1))*(1 + 2*self.metric(x2, x2))))
def _get_compiled_theano_functions(N_QUAD_PTS):
# Planet masses: m1,m2
m1, m2 = T.dscalars(2)
mstar = 1
mu1 = m1 * mstar / (mstar + m1)
mu2 = m2 * mstar / (mstar + m2)
Mstar1 = mstar + m1
Mstar2 = mstar + m2
beta1 = mu1 * T.sqrt(Mstar1 / mstar) / (mu1 + mu2)
beta2 = mu2 * T.sqrt(Mstar2 / mstar) / (mu1 + mu2)
j, k = T.lscalars('jk')
s = (j - k) / k
# Angle variable for averaging over
psi = T.dvector()
# Quadrature weights
quad_weights = T.dvector('w')
# Dynamical variables:
Ndof = 3
Nconst = 1
dyvars = T.vector()
y1, y2, y_inc, x1, x2, x_inc, amd = [
dyvars[i] for i in range(2 * Ndof + Nconst)
]
a20 = T.constant(1.)
a10 = ((j - k) / j)**(2 / 3) * (Mstar1 / Mstar2)**(1 / 3)
L10 = beta1 * T.sqrt(a10)
L20 = beta2 * T.sqrt(a20)
Ltot = L10 + L20
f = L10 / L20
L2res = (Ltot + amd) / (1 + f)
Psi = -k * (s * L2res + (1 + s) * f * L2res)
###
# actions
###
I1 = 0.5 * (x1 * x1 + y1 * y1)
I2 = 0.5 * (x2 * x2 + y2 * y2)
Phi = 0.5 * (x_inc * x_inc + y_inc * y_inc)
L1 = -s * Ltot - Psi / k - s * (I1 + I2 + Phi)
L2 = (1 + s) * Ltot + Psi / k + (1 + s) * (I1 + I2 + Phi)
# Set lambda2=0
l2 = T.constant(0.)
l1 = -1 * k * psi
theta_res = (1 + s) * l2 - s * l1
cos_theta_res = T.cos(theta_res)
sin_theta_res = T.sin(theta_res)
kappa1 = x1 * cos_theta_res + y1 * sin_theta_res
eta1 = y1 * cos_theta_res - x1 * sin_theta_res
kappa2 = x2 * cos_theta_res + y2 * sin_theta_res
eta2 = y2 * cos_theta_res - x2 * sin_theta_res
sigma = x_inc * cos_theta_res + y_inc * sin_theta_res
rho = y_inc * cos_theta_res - x_inc * sin_theta_res
# y = (sigma-i*rho)/sqrt(2)
# = sqrt(Phi) * exp[i (Omega1+Omega2) / 2]
# Malige+ 2002, Eqs 20 and 21
r2byr1 = (L2 - L1 - I2 + I1) / Ltot
sigma1 = rho * T.sqrt(1 + r2byr1) / T.sqrt(2)
sigma2 = -rho * T.sqrt(1 - r2byr1) / T.sqrt(2)
rho1 = -sigma * T.sqrt(1 + r2byr1) / T.sqrt(2)
rho2 = sigma * T.sqrt(1 - r2byr1) / T.sqrt(2)
Xre1 = kappa1 / T.sqrt(L1)
Xim1 = -eta1 / T.sqrt(L1)
Yre1 = 0.5 * sigma1 / T.sqrt(L1)
Yim1 = -0.5 * rho1 / T.sqrt(L1)
Xre2 = kappa2 / T.sqrt(L2)
Xim2 = -eta2 / T.sqrt(L2)
Yre2 = 0.5 * sigma2 / T.sqrt(L2)
Yim2 = -0.5 * rho2 / T.sqrt(L2)
absX1_sq = 2 * I1 / L1
absX2_sq = 2 * I2 / L2
X_to_z1 = T.sqrt(1 - absX1_sq / 4)
X_to_z2 = T.sqrt(1 - absX2_sq / 4)
Y_to_zeta1 = 1 / T.sqrt(1 - absX1_sq / 2)
Y_to_zeta2 = 1 / T.sqrt(1 - absX2_sq / 2)
a1 = (L1 / beta1)**2
k1 = Xre1 * X_to_z1
h1 = Xim1 * X_to_z1
q1 = Yre1 * Y_to_zeta1
p1 = Yim1 * Y_to_zeta1
e1 = T.sqrt(absX1_sq) * X_to_z1
inc1 = 2 * T.arcsin(T.sqrt(p1 * p1 + q1 * q1))
a2 = (L2 / beta2)**2
k2 = Xre2 * X_to_z2
h2 = Xim2 * X_to_z2
q2 = Yre2 * Y_to_zeta2
p2 = Yim2 * Y_to_zeta2
e2 = T.sqrt(absX2_sq) * X_to_z2
inc2 = 2 * T.arcsin(T.sqrt(p2 * p2 + q2 * q2))
beta1p = T.sqrt(Mstar1) * beta1
beta2p = T.sqrt(Mstar2) * beta2
Hkep = -0.5 * beta1p / a1 - 0.5 * beta2p / a2
Hdir, Hind = calc_Hint_components_spatial(a1, a2, l1, l2, h1, k1, h2, k2,
p1, q1, p2, q2, Mstar1, Mstar2)
eps = m1 * m2 / (mu1 + mu2) / T.sqrt(mstar)
Hpert = (Hdir + Hind / mstar)
Hpert_av = Hpert.dot(quad_weights)
Htot = Hkep + eps * Hpert_av
#####################################################
# Set parameters for compiling functions with Theano
#####################################################
# Get numerical quadrature nodes and weights
nodes, weights = np.polynomial.legendre.leggauss(N_QUAD_PTS)
# Rescale for integration interval from [-1,1] to [-pi,pi]
nodes = nodes * np.pi
weights = weights * 0.5
# 'givens' will fix some parameters of Theano functions compiled below
givens = [(psi, nodes), (quad_weights, weights)]
# 'ins' will set the inputs of Theano functions compiled below
# Note: 'extra_ins' will be passed as values of object attributes
# of the 'ResonanceEquations' class 'defined below
extra_ins = [m1, m2, j, k]
ins = [dyvars] + extra_ins
Stilde = Phi * (L2 - I2 - L1 + I1) / (Ltot)
Q1 = 0.5 * (Phi + Stilde)
Q2 = 0.5 * (Phi - Stilde)
inc1 = T.arccos(1 - Q1 / (L1 - I1))
inc2 = T.arccos(1 - Q2 / (L2 - I2))
orbels = [
a1, e1, inc1, k * T.arctan2(y1, x1), a2, e2, inc2,
k * T.arctan2(y2, x2),
T.arctan2(y_inc, x_inc)
]
orbels_dict = dict(
zip([
'a1', 'e1', 'inc1', 'theta1', 'a2', 'e2', 'inc2', 'theta2', 'phi'
], orbels))
actions = [L1, L2, I1, I2, Q1, Q2]
actions_dict = dict(
zip(['L1', 'L2', 'Gamma1', 'Gamma2', 'Q1', 'Q2'], actions))
# Conservative flow
gradHtot = T.grad(Htot, wrt=dyvars)
gradHpert = T.grad(Hpert_av, wrt=dyvars)
gradHkep = T.grad(Hkep, wrt=dyvars)
hessHtot = theano.gradient.hessian(Htot, wrt=dyvars)
hessHpert = theano.gradient.hessian(Hpert_av, wrt=dyvars)
hessHkep = theano.gradient.hessian(Hkep, wrt=dyvars)
Jtens = T.as_tensor(np.pad(getOmegaMatrix(Ndof), (0, Nconst), 'constant'))
H_flow_vec = Jtens.dot(gradHtot)
Hpert_flow_vec = Jtens.dot(gradHpert)
Hkep_flow_vec = Jtens.dot(gradHkep)
H_flow_jac = Jtens.dot(hessHtot)
Hpert_flow_jac = Jtens.dot(hessHpert)
Hkep_flow_jac = Jtens.dot(hessHkep)
##########################
# Compile Theano functions
##########################
func_dict = {
# Hamiltonians
'H': Htot,
#'Hpert':Hpert_av,
#'Hkep':Hkep,
## Hamiltonian flows
'H_flow': H_flow_vec,
#'Hpert_flow':Hpert_flow_vec,
#'Hkep_flow':Hkep_flow_vec,
## Hamiltonian flow Jacobians
'H_flow_jac': H_flow_jac,
#'Hpert_flow_jac':Hpert_flow_jac,
#'Hkep_flow_jac':Hkep_flow_jac,
## Extras
'orbital_elements': orbels_dict,
'actions': actions_dict
}
compiled_func_dict = dict()
with tqdm(func_dict.items()) as t:
for key, val in t:
t.set_description("Compiling '{}'".format(key))
if key is 'timescales':
inputs = extra_ins
else:
inputs = ins
cf = theano.function(inputs=inputs,
outputs=val,
givens=givens,
on_unused_input='ignore')
compiled_func_dict[key] = cf
return compiled_func_dict
data = pd.read_csv(io.StringIO(golf_data), sep=" ")
#model-inference
coords = {"distance": data.distance}
fileName='golf_geometry_PyMC3'
samples=2000
chains=2
tune=1000
geometry_model=pm.Model(coords=coords)
with geometry_model:
#to store the n-parameter of Binomial dist
#in the constant group of ArviZ InferenceData
#You should always call it n for imd to retrieve it
n = pm.Data('n', data.tries)
sigma_angle = pm.HalfNormal('sigma_angle')
p_goes_in = pm.Deterministic('p_goes_in', 2 * Phi(tt.arcsin((CUP_RADIUS - BALL_RADIUS) / data.distance) / sigma_angle) - 1, dims='distance')
successes = pm.Binomial('successes', n=n, p=p_goes_in, observed=data.successes, dims='distance')
#inference
trace_g = pm.sample(draws=samples, chains=chains, tune=tune)
prior_g= pm.sample_prior_predictive(samples=samples)
posterior_predictive_g = pm.sample_posterior_predictive(trace_g,samples=samples)
## STEP 1
# will also capture all the sampler statistics
data_g = az.from_pymc3(trace=trace_g, prior=prior_g, posterior_predictive=posterior_predictive_g)
## STEP 2
#dag
dag_g = get_dag(geometry_model)
# insert dag into sampler stat attributes
data_g.sample_stats.attrs["graph"] = str(dag_g)
def bound_loss(x, tnp=np):
eps = 1e-9
loss = tnp.maximum(tnp.maximum(eps, x - 1), tnp.maximum(eps, -x)) + eps
return tnp.maximum(loss, eps) + eps
params_plus1 = shared(np.random.rand(nbatch, 2))
params_plus2 = shared(np.random.rand(nbatch, 2))
a = Print("invplus(x, params_plus1")(invplus(x, params_plus1))
b = Print("invplus(x, params_plus2")(invplus(y, params_plus2))
eps = 1e-9
a2 = T.arccos(T.clip(a, eps, 1 - eps))
b2 = T.arcsin(T.clip(b, eps, 1 - eps))
bl1 = bound_loss(a, tnp=T)
bl2 = bound_loss(b, tnp=T)
phi1_group = []
phi2_group = []
phi3_group = []
phi1_group.append(a2[:, 0])
phi1_group.append(b2[:, 0])
delta_group = []
delta_group.append(a2[:, 1])
delta_group.append(b2[:, 1])
delta_single, delta_var = singular(delta_group, name="delta")
params_plus3 = shared(np.random.rand(nbatch, 1))
def run_onetransit_inference(self, prior_d, pklpath, make_threadsafe=True):
"""
Similar to "run_transit_inference", but with more restrictive priors on
ephemeris. Also, it simultaneously fits for quadratic trend.
"""
# if the model has already been run, pull the result from the
# pickle. otherwise, run it.
if os.path.exists(pklpath):
d = pickle.load(open(pklpath, 'rb'))
self.model = d['model']
self.trace = d['trace']
self.map_estimate = d['map_estimate']
return 1
with pm.Model() as model:
assert len(self.data.keys()) == 1
name = list(self.data.keys())[0]
x_obs = list(self.data.values())[0][0]
y_obs = list(self.data.values())[0][1]
y_err = list(self.data.values())[0][2]
t_exp = list(self.data.values())[0][3]
# Fixed data errors.
sigma = y_err
# Define priors and PyMC3 random variables to sample over.
# Stellar parameters. (Following tess.world notebooks).
logg_star = pm.Normal("logg_star", mu=LOGG, sd=LOGG_STDEV)
r_star = pm.Bound(pm.Normal, lower=0.0)("r_star",
mu=RSTAR,
sd=RSTAR_STDEV)
rho_star = pm.Deterministic("rho_star",
factor * 10**logg_star / r_star)
# Transit parameters.
t0 = pm.Normal("t0",
mu=prior_d['t0'],
sd=1e-3,
testval=prior_d['t0'])
period = pm.Normal('period',
mu=prior_d['period'],
sd=3e-4,
testval=prior_d['period'])
# NOTE: might want to implement kwarg for flexibility
# u = xo.distributions.QuadLimbDark(
# "u", testval=prior_d['u']
# )
u0 = pm.Uniform('u[0]',
lower=prior_d['u[0]'] - 0.15,
upper=prior_d['u[0]'] + 0.15,
testval=prior_d['u[0]'])
u1 = pm.Uniform('u[1]',
lower=prior_d['u[1]'] - 0.15,
upper=prior_d['u[1]'] + 0.15,
testval=prior_d['u[1]'])
u = [u0, u1]
# # The Espinoza (2018) parameterization for the joint radius ratio and
# # impact parameter distribution
# r, b = xo.distributions.get_joint_radius_impact(
# min_radius=0.001, max_radius=1.0,
# testval_r=prior_d['r'],
# testval_b=prior_d['b']
# )
# # NOTE: apparently, it's been deprecated. DFM's manuscript notes
# that it leads to Rp/Rs values biased high
log_r = pm.Uniform('log_r',
lower=np.log(1e-2),
upper=np.log(1),
testval=prior_d['log_r'])
r = pm.Deterministic('r', tt.exp(log_r))
b = xo.distributions.ImpactParameter("b",
ror=r,
testval=prior_d['b'])
# the transit
orbit = xo.orbits.KeplerianOrbit(period=period,
t0=t0,
b=b,
rho_star=rho_star)
transit_lc = pm.Deterministic(
'transit_lc',
xo.LimbDarkLightCurve(u).get_light_curve(
orbit=orbit, r=r, t=x_obs, texp=t_exp).T.flatten())
# quadratic trend parameters
mean = pm.Normal(f"{name}_mean",
mu=prior_d[f'{name}_mean'],
sd=1e-2,
testval=prior_d[f'{name}_mean'])
a1 = pm.Normal(f"{name}_a1",
mu=prior_d[f'{name}_a1'],
sd=1,
testval=prior_d[f'{name}_a1'])
a2 = pm.Normal(f"{name}_a2",
mu=prior_d[f'{name}_a2'],
sd=1,
testval=prior_d[f'{name}_a2'])
_tmid = np.nanmedian(x_obs)
lc_model = pm.Deterministic(
'mu_transit', mean + a1 * (x_obs - _tmid) + a2 *
(x_obs - _tmid)**2 + transit_lc)
roughdepth = pm.Deterministic(f'roughdepth',
pm.math.abs_(transit_lc).max())
#
# Derived parameters
#
# planet radius in jupiter radii
r_planet = pm.Deterministic(
"r_planet",
(r * r_star) * (1 * units.Rsun / (1 * units.Rjup)).cgs.value)
#
# eq 30 of winn+2010, ignoring planet density.
#
a_Rs = pm.Deterministic("a_Rs", (rho_star * period**2)**(1 / 3) *
(((1 * units.gram / (1 * units.cm)**3) *
(1 * units.day**2) * const.G /
(3 * np.pi))**(1 / 3)).cgs.value)
#
# cosi. assumes e=0 (e.g., Winn+2010 eq 7)
#
cosi = pm.Deterministic("cosi", b / a_Rs)
# safer than tt.arccos(cosi)
sini = pm.Deterministic("sini", pm.math.sqrt(1 - cosi**2))
#
# transit durations (T_14, T_13) for circular orbits. Winn+2010 Eq 14, 15.
# units: hours.
#
T_14 = pm.Deterministic('T_14', (period / np.pi) * tt.arcsin(
(1 / a_Rs) * pm.math.sqrt((1 + r)**2 - b**2) * (1 / sini)) *
24)
T_13 = pm.Deterministic('T_13', (period / np.pi) * tt.arcsin(
(1 / a_Rs) * pm.math.sqrt((1 - r)**2 - b**2) * (1 / sini)) *
24)
#
# mean model and likelihood
#
# mean_model = mu_transit + mean
# mu_model = pm.Deterministic('mu_model', lc_model)
likelihood = pm.Normal('obs',
mu=lc_model,
sigma=sigma,
observed=y_obs)
# Optimizing
map_estimate = pm.find_MAP(model=model)
# start = model.test_point
# if 'transit' in self.modelcomponents:
# map_estimate = xo.optimize(start=start,
# vars=[r, b, period, t0])
# map_estimate = xo.optimize(start=map_estimate)
if make_threadsafe:
pass
else:
# as described in
# https://github.com/matplotlib/matplotlib/issues/15410
# matplotlib is not threadsafe. so do not make plots before
# sampling, because some child processes tries to close a
# cached file, and crashes the sampler.
print(map_estimate)
# sample from the posterior defined by this model.
trace = pm.sample(
tune=self.N_samples,
draws=self.N_samples,
start=map_estimate,
cores=self.N_cores,
chains=self.N_chains,
step=xo.get_dense_nuts_step(target_accept=0.8),
)
with open(pklpath, 'wb') as buff:
pickle.dump(
{
'model': model,
'trace': trace,
'map_estimate': map_estimate
}, buff)
self.model = model
self.trace = trace
self.map_estimate = map_estimate
def run_alltransit_inference(self, prior_d, pklpath, make_threadsafe=True):
# if the model has already been run, pull the result from the
# pickle. otherwise, run it.
if os.path.exists(pklpath):
d = pickle.load(open(pklpath, 'rb'))
self.model = d['model']
self.trace = d['trace']
self.map_estimate = d['map_estimate']
return 1
with pm.Model() as model:
# Shared parameters
# Stellar parameters. (Following tess.world notebooks).
logg_star = pm.Normal("logg_star", mu=LOGG, sd=LOGG_STDEV)
r_star = pm.Bound(pm.Normal, lower=0.0)("r_star",
mu=RSTAR,
sd=RSTAR_STDEV)
rho_star = pm.Deterministic("rho_star",
factor * 10**logg_star / r_star)
# fix Rp/Rs across bandpasses, b/c you're assuming it's a planet
if 'quaddepthvar' not in self.modelid:
log_r = pm.Uniform('log_r',
lower=np.log(1e-2),
upper=np.log(1),
testval=prior_d['log_r'])
r = pm.Deterministic('r', tt.exp(log_r))
else:
log_r_Tband = pm.Uniform('log_r_Tband',
lower=np.log(1e-2),
upper=np.log(1),
testval=prior_d['log_r_Tband'])
r_Tband = pm.Deterministic('r_Tband', tt.exp(log_r_Tband))
log_r_Rband = pm.Uniform('log_r_Rband',
lower=np.log(1e-2),
upper=np.log(1),
testval=prior_d['log_r_Rband'])
r_Rband = pm.Deterministic('r_Rband', tt.exp(log_r_Rband))
log_r_Bband = pm.Uniform('log_r_Bband',
lower=np.log(1e-2),
upper=np.log(1),
testval=prior_d['log_r_Bband'])
r_Bband = pm.Deterministic('r_Bband', tt.exp(log_r_Bband))
r = r_Tband
# Some orbital parameters
t0 = pm.Normal("t0",
mu=prior_d['t0'],
sd=5e-3,
testval=prior_d['t0'])
period = pm.Normal('period',
mu=prior_d['period'],
sd=5e-3,
testval=prior_d['period'])
b = xo.distributions.ImpactParameter("b",
ror=r,
testval=prior_d['b'])
orbit = xo.orbits.KeplerianOrbit(period=period,
t0=t0,
b=b,
rho_star=rho_star)
# NOTE: limb-darkening should be bandpass specific, but we don't
# have the SNR to justify that, so go with TESS-dominated
u0 = pm.Uniform('u[0]',
lower=prior_d['u[0]'] - 0.15,
upper=prior_d['u[0]'] + 0.15,
testval=prior_d['u[0]'])
u1 = pm.Uniform('u[1]',
lower=prior_d['u[1]'] - 0.15,
upper=prior_d['u[1]'] + 0.15,
testval=prior_d['u[1]'])
u = [u0, u1]
star = xo.LimbDarkLightCurve(u)
# Loop over "instruments" (TESS, then each ground-based lightcurve)
parameters = dict()
lc_models = dict()
roughdepths = dict()
for n, (name, (x, y, yerr, texp)) in enumerate(self.data.items()):
# Define per-instrument parameters in a submodel, to not need
# to prefix the names. Yields e.g., "TESS_mean",
# "elsauce_0_mean", "elsauce_2_a2"
with pm.Model(name=name, model=model):
# Transit parameters.
mean = pm.Normal("mean",
mu=prior_d[f'{name}_mean'],
sd=1e-2,
testval=prior_d[f'{name}_mean'])
if 'quad' in self.modelid:
if name != 'tess':
# units: rel flux per day.
a1 = pm.Normal("a1",
mu=prior_d[f'{name}_a1'],
sd=1,
testval=prior_d[f'{name}_a1'])
# units: rel flux per day^2.
a2 = pm.Normal("a2",
mu=prior_d[f'{name}_a2'],
sd=1,
testval=prior_d[f'{name}_a2'])
if self.modelid == 'alltransit':
lc_models[name] = pm.Deterministic(
f'{name}_mu_transit', mean + star.get_light_curve(
orbit=orbit, r=r, t=x, texp=texp).T.flatten())
elif self.modelid == 'alltransit_quad':
if name != 'tess':
# midpoint for this definition of the quadratic trend
_tmid = np.nanmedian(x)
lc_models[name] = pm.Deterministic(
f'{name}_mu_transit', mean + a1 * (x - _tmid) +
a2 * (x - _tmid)**2 + star.get_light_curve(
orbit=orbit, r=r, t=x, texp=texp).T.flatten())
elif name == 'tess':
lc_models[name] = pm.Deterministic(
f'{name}_mu_transit', mean + star.get_light_curve(
orbit=orbit, r=r, t=x, texp=texp).T.flatten())
elif self.modelid == 'alltransit_quaddepthvar':
if name != 'tess':
# midpoint for this definition of the quadratic trend
_tmid = np.nanmedian(x)
# do custom depth-to-
if (name == 'elsauce_20200401'
or name == 'elsauce_20200426'):
r = r_Rband
elif name == 'elsauce_20200521':
r = r_Tband
elif name == 'elsauce_20200614':
r = r_Bband
transit_lc = star.get_light_curve(
orbit=orbit, r=r, t=x, texp=texp).T.flatten()
lc_models[name] = pm.Deterministic(
f'{name}_mu_transit', mean + a1 * (x - _tmid) +
a2 * (x - _tmid)**2 + transit_lc)
roughdepths[name] = pm.Deterministic(
f'{name}_roughdepth',
pm.math.abs_(transit_lc).max())
elif name == 'tess':
r = r_Tband
transit_lc = star.get_light_curve(
orbit=orbit, r=r, t=x, texp=texp).T.flatten()
lc_models[name] = pm.Deterministic(
f'{name}_mu_transit', mean + transit_lc)
roughdepths[name] = pm.Deterministic(
f'{name}_roughdepth',
pm.math.abs_(transit_lc).max())
# TODO: add error bar fudge
likelihood = pm.Normal(f'{name}_obs',
mu=lc_models[name],
sigma=yerr,
observed=y)
#
# Derived parameters
#
if self.modelid == 'alltransit_quaddepthvar':
r = r_Tband
# planet radius in jupiter radii
r_planet = pm.Deterministic(
"r_planet",
(r * r_star) * (1 * units.Rsun / (1 * units.Rjup)).cgs.value)
#
# eq 30 of winn+2010, ignoring planet density.
#
a_Rs = pm.Deterministic("a_Rs", (rho_star * period**2)**(1 / 3) *
(((1 * units.gram / (1 * units.cm)**3) *
(1 * units.day**2) * const.G /
(3 * np.pi))**(1 / 3)).cgs.value)
#
# cosi. assumes e=0 (e.g., Winn+2010 eq 7)
#
cosi = pm.Deterministic("cosi", b / a_Rs)
# probably safer than tt.arccos(cosi)
sini = pm.Deterministic("sini", pm.math.sqrt(1 - cosi**2))
#
# transit durations (T_14, T_13) for circular orbits. Winn+2010 Eq 14, 15.
# units: hours.
#
T_14 = pm.Deterministic('T_14', (period / np.pi) * tt.arcsin(
(1 / a_Rs) * pm.math.sqrt((1 + r)**2 - b**2) * (1 / sini)) *
24)
T_13 = pm.Deterministic('T_13', (period / np.pi) * tt.arcsin(
(1 / a_Rs) * pm.math.sqrt((1 - r)**2 - b**2) * (1 / sini)) *
24)
# Optimizing
map_estimate = pm.find_MAP(model=model)
# start = model.test_point
# if 'transit' in self.modelcomponents:
# map_estimate = xo.optimize(start=start,
# vars=[r, b, period, t0])
# map_estimate = xo.optimize(start=map_estimate)
if make_threadsafe:
pass
else:
# NOTE: would usually plot MAP estimate here, but really
# there's not a huge need.
print(map_estimate)
pass
# sample from the posterior defined by this model.
trace = pm.sample(
tune=self.N_samples,
draws=self.N_samples,
start=map_estimate,
cores=self.N_cores,
chains=self.N_chains,
step=xo.get_dense_nuts_step(target_accept=0.8),
)
with open(pklpath, 'wb') as buff:
pickle.dump(
{
'model': model,
'trace': trace,
'map_estimate': map_estimate
}, buff)
self.model = model
self.trace = trace
self.map_estimate = map_estimate
def run_allindivtransit_inference(self,
prior_d,
pklpath,
make_threadsafe=True,
target_accept=0.8):
# if the model has already been run, pull the result from the
# pickle. otherwise, run it.
if os.path.exists(pklpath):
d = pickle.load(open(pklpath, 'rb'))
self.model = d['model']
self.trace = d['trace']
self.map_estimate = d['map_estimate']
return 1
with pm.Model() as model:
# Shared parameters
# Stellar parameters. (Following tess.world notebooks).
logg_star = pm.Normal("logg_star", mu=LOGG, sd=LOGG_STDEV)
r_star = pm.Bound(pm.Normal, lower=0.0)("r_star",
mu=RSTAR,
sd=RSTAR_STDEV)
rho_star = pm.Deterministic("rho_star",
factor * 10**logg_star / r_star)
# fix Rp/Rs across bandpasses, b/c you're assuming it's a planet
log_r = pm.Uniform('log_r',
lower=np.log(1e-2),
upper=np.log(1),
testval=prior_d['log_r'])
r = pm.Deterministic('r', tt.exp(log_r))
# Some orbital parameters
t0 = pm.Normal("t0",
mu=prior_d['t0'],
sd=1e-1,
testval=prior_d['t0'])
period = pm.Normal('period',
mu=prior_d['period'],
sd=1e-1,
testval=prior_d['period'])
b = xo.distributions.ImpactParameter("b",
ror=r,
testval=prior_d['b'])
orbit = xo.orbits.KeplerianOrbit(period=period,
t0=t0,
b=b,
rho_star=rho_star)
# NOTE: limb-darkening should be bandpass specific, but we don't
# have the SNR to justify that, so go with TESS-dominated
# u = xo.QuadLimbDark("u")
# NOTE: deprecated(?)
delta_u = 0.15
u0 = pm.Uniform('u[0]',
lower=prior_d['u[0]'] - delta_u,
upper=prior_d['u[0]'] + delta_u,
testval=prior_d['u[0]'])
u1 = pm.Uniform('u[1]',
lower=prior_d['u[1]'] - delta_u,
upper=prior_d['u[1]'] + delta_u,
testval=prior_d['u[1]'])
u = [u0, u1]
star = xo.LimbDarkLightCurve(u)
# Loop over "instruments" (TESS, then each ground-based lightcurve)
parameters = dict()
lc_models = dict()
roughdepths = dict()
for n, (name, (x, y, yerr, texp)) in enumerate(self.data.items()):
if 'tess' in name:
delta_trend = 0.100
else:
delta_trend = 0.050
# Define per-instrument parameters in a submodel, to not need
# to prefix the names. Yields e.g., "TESS_0_mean",
# "elsauce_0_mean", "elsauce_2_a2"
mean = pm.Normal(f'{name}_mean',
mu=prior_d[f'{name}_mean'],
sd=1e-2,
testval=prior_d[f'{name}_mean'])
a1 = pm.Uniform(f'{name}_a1',
lower=-delta_trend,
upper=delta_trend,
testval=prior_d[f'{name}_a1'])
a2 = pm.Uniform(f'{name}_a2',
lower=-delta_trend,
upper=delta_trend,
testval=prior_d[f'{name}_a2'])
# midpoint for this definition of the quadratic trend
_tmid = np.nanmedian(x)
transit_lc = star.get_light_curve(orbit=orbit,
r=r,
t=x,
texp=texp).T.flatten()
lc_models[name] = pm.Deterministic(
f'{name}_mu_transit',
mean + a1 * (x - _tmid) + a2 * (x - _tmid)**2 + transit_lc)
roughdepths[name] = pm.Deterministic(
f'{name}_roughdepth',
pm.math.abs_(transit_lc).max())
# NOTE: might want error bar fudge.
likelihood = pm.Normal(f'{name}_obs',
mu=lc_models[name],
sigma=yerr,
observed=y)
#
# Derived parameters
#
# planet radius in jupiter radii
r_planet = pm.Deterministic(
"r_planet",
(r * r_star) * (1 * units.Rsun / (1 * units.Rjup)).cgs.value)
#
# eq 30 of winn+2010, ignoring planet density.
#
a_Rs = pm.Deterministic("a_Rs", (rho_star * period**2)**(1 / 3) *
(((1 * units.gram / (1 * units.cm)**3) *
(1 * units.day**2) * const.G /
(3 * np.pi))**(1 / 3)).cgs.value)
#
# cosi. assumes e=0 (e.g., Winn+2010 eq 7)
#
cosi = pm.Deterministic("cosi", b / a_Rs)
# probably safer than tt.arccos(cosi)
sini = pm.Deterministic("sini", pm.math.sqrt(1 - cosi**2))
#
# transit durations (T_14, T_13) for circular orbits. Winn+2010 Eq 14, 15.
# units: hours.
#
T_14 = pm.Deterministic('T_14', (period / np.pi) * tt.arcsin(
(1 / a_Rs) * pm.math.sqrt((1 + r)**2 - b**2) * (1 / sini)) *
24)
T_13 = pm.Deterministic('T_13', (period / np.pi) * tt.arcsin(
(1 / a_Rs) * pm.math.sqrt((1 - r)**2 - b**2) * (1 / sini)) *
24)
map_estimate = pm.find_MAP(model=model)
# if make_threadsafe:
# pass
# else:
# # NOTE: would usually plot MAP estimate here, but really
# # there's not a huge need.
# print(map_estimate)
# for k,v in map_estimate.items():
# if 'transit' not in k:
# print(k, v)
# NOTE: could start at map_estimate, which currently is not being
# used for anything.
start = model.test_point
trace = pm.sample(
tune=self.N_samples,
draws=self.N_samples,
start=start,
cores=self.N_cores,
chains=self.N_chains,
step=xo.get_dense_nuts_step(target_accept=target_accept),
)
with open(pklpath, 'wb') as buff:
pickle.dump(
{
'model': model,
'trace': trace,
'map_estimate': map_estimate
}, buff)
self.model = model
self.trace = trace
self.map_estimate = map_estimate
def asin(x): return T.arcsin(x)
def _compile_model(self):
""" theano implementation of 3C model """
### GC90 atmospheric model implementation
theta_sun, beta, alpha, am, rh, pressure = T.scalars(
'theta_sun', 'beta', 'alpha', 'am', 'rh', 'pressure')
wl = T.vector('wl')
wl_a = 550
theta_sun_ = theta_sun * np.pi / 180.
z3 = -0.1417 * alpha + 0.82
z2 = ifelse(T.gt(alpha, 1.2), 0.65, z3)
z1 = ifelse(T.lt(alpha, 0), 0.82, z2)
theta_sun_mean = z1
B3 = T.log(1 - theta_sun_mean)
B2 = B3 * (0.0783 + B3 * (-0.3824 - 0.5874 * B3))
B1 = B3 * (1.459 + B3 * (0.1595 + 0.4129 * B3))
Fa = 1 - 0.5 * T.exp((B1 + B2 * T.cos(theta_sun_)) * T.cos(theta_sun_))
omega_a = (-0.0032 * am + 0.972) * T.exp(3.06 * 1e-4 * rh)
tau_a = beta * (wl / wl_a)**(-alpha)
# fixed a bug in M, thanks Jaime! [brackets added]
M = 1 / (T.cos(theta_sun_) + 0.50572 *
(90 + 6.07995 - theta_sun)**(-1.6364))
M_ = M * pressure / 1013.25
Tr = T.exp(-M_ / (115.6406 * (wl / 1000)**4 - 1.335 * (wl / 1000)**2))
Tas = T.exp(-omega_a * tau_a * M)
Edd = Tr * Tas
Edsr = 0.5 * (1 - Tr**0.95)
Edsa = Tr**1.5 * (1 - Tas) * Fa
Ed = Edd + Edsr + Edsa
Edd_Ed = Edd / Ed
Edsr_Ed = Edsr / Ed
Edsa_Ed = Edsa / Ed
Eds_Ed = Edsr_Ed + Edsa_Ed
### Albert and Mobley bio-optical model implementation
a_w, daw_dT, astar_ph, astar_y, Ls_Ed = T.vectors(
'a_w', 'daw_dT', 'astar_ph', 'astar_y', 'Ls_Ed')
C_chl, C_sm, C_mie, n_mie, C_y, S_y, T_w, theta_view, n_w, rho_s, rho_dd, rho_ds, delta = T.scalars(
'C_chl', 'C_sm', 'C_mie', 'n_mie', 'C_y', 'S_y', 'T_w',
'theta_view', 'n_w', 'rho_s', 'rho_dd', 'rho_ds', 'delta')
# calc_a_ph
a_ph = C_chl * astar_ph
# calc_a_y
wl_ref_y = 440
a_y = ifelse(T.eq(S_y, -1), C_y * astar_y,
C_y * T.exp(-S_y * (wl - wl_ref_y)))
# calc_a
T_w_ref = 20.
a_w_corr = a_w + (T_w - T_w_ref) * daw_dT
a = a_w_corr + a_ph + a_y
# calc_bb_sm
bbstar_sm = 0.0086
bbstar_mie = 0.0042
wl_ref_mie = 500
bb_sm = C_sm * bbstar_sm + C_mie * bbstar_mie * (wl /
wl_ref_mie)**n_mie
# calc_bb
b1 = ifelse(T.eq(n_w, 1.34), 0.00144, 0.00111)
wl_ref_water = 500
S_water = -4.32
bb_water = b1 * (wl / wl_ref_water)**S_water
bb = bb_water + bb_sm
# calc omega_b
omega_b = bb / (bb + a)
# calc sun and viewing zenith angles under water
theta_sun_ = theta_sun * np.pi / 180.
theta_sun_ss = T.arcsin(T.sin(theta_sun_) / n_w)
theta_view_ = theta_view * np.pi / 180.
theta_view_ss = T.arcsin(T.sin(theta_view_) / n_w)
p_f = [0.1034, 1, 3.3586, -6.5358, 4.6638, 2.4121]
p_frs = [0.0512, 1, 4.6659, -7.8387, 5.4571, 0.1098, 0.4021]
# calc subsurface reflectance
f = p_f[0] * (p_f[1] + p_f[2] * omega_b + p_f[3] * omega_b**2 +
p_f[4] * omega_b**3) * (1 + p_f[5] / T.cos(theta_sun_ss))
R0minus = f * omega_b
# calc subsurface remote sensing reflectance
frs = p_frs[0] * (p_frs[1] + p_frs[2] * omega_b +
p_frs[3] * omega_b**2 + p_frs[4] * omega_b**3) * (
1 + p_frs[5] / T.cos(theta_sun_ss)) * (
1 + p_frs[6] / T.cos(theta_view_ss))
Rrs0minus = frs * omega_b
# calc water surface reflected reflectance
Rrs_refl = rho_s * Ls_Ed + rho_dd * Edd_Ed / np.pi + rho_ds * Eds_Ed / np.pi + delta
# calc_Rrs0plus (Lee1998, eq22), R=Q*Rrs
gamma = 0.48
zeta = 0.518
Rrs = zeta * Rrs0minus / (1 - gamma * R0minus)
Lu_Ed = Rrs + Rrs_refl
f = th.function([
beta, alpha, am, rh, pressure, C_chl, C_sm, C_mie, n_mie, C_y, S_y,
T_w, theta_sun, theta_view, n_w, rho_s, rho_dd, rho_ds, delta, wl,
a_w, daw_dT, astar_ph, astar_y, Ls_Ed
], [Rrs, Rrs_refl, Lu_Ed, Ed],
on_unused_input='warn')
return f
# return T.mean(s, axis=0), variance # T.maximum(T.var(s, axis=0), eps) # Should eps be here?!
def bound_loss(x, tnp = np) :
eps = 1e-9
loss = tnp.maximum(tnp.maximum(eps,x-1), tnp.maximum(eps,-x)) + eps
return tnp.maximum(loss, eps) + eps
params_plus1 = shared(np.random.rand(nbatch, 2))
params_plus2 = shared(np.random.rand(nbatch, 2))
a = Print('invplus(x, params_plus1')(invplus(x, params_plus1))
b = Print('invplus(x, params_plus2')(invplus(y, params_plus2))
eps = 1e-9
a2 = T.arccos(T.clip(a, eps, 1))
b2 = T.arcsin(T.clip(b, eps, 1))
bl1 = bound_loss(a, tnp = T)
bl2 = bound_loss(b, tnp = T)
theta1_group = []
theta2_group = []
theta3_group = []
theta1_group.append(a2[:, 0])
theta1_group.append(b2[:, 0])
delta_group = []
delta_group.append(a2[:, 1])
delta_group.append(b2[:, 1])
delta_single, delta_var = singular(delta_group, name = 'delta')
params_plus3 = shared(np.random.rand(nbatch, 1))