def test_apply_inverse(solver, seed=1234, N=201, yerr=0.1):
np.random.seed(seed)
# Set up the solver.
kernel = 1.0 * kernels.ExpSquaredKernel(0.5)
kwargs = dict()
if solver == HODLRSolver:
kwargs["tol"] = 1e-10
gp = GP(kernel, solver=solver, **kwargs)
# Sample some data.
x = np.sort(np.random.rand(N))
y = gp.sample(x)
gp.compute(x, yerr=yerr)
K = gp.get_matrix(x)
K[np.diag_indices_from(K)] += yerr**2
b1 = np.linalg.solve(K, y)
b2 = gp.apply_inverse(y)
assert np.allclose(b1, b2)
y = gp.sample(x, size=5).T
b1 = np.linalg.solve(K, y)
b2 = gp.apply_inverse(y)
assert np.allclose(b1, b2)
def test_predict_single(solver, seed=1234, N=201, yerr=0.1):
np.random.seed(seed)
# Set up the solver.
kernel = 1.0 * kernels.ExpSquaredKernel(0.5)
kwargs = dict()
if solver == HODLRSolver:
kwargs["tol"] = 1e-8
gp = GP(kernel, solver=solver, **kwargs)
x = np.sort(np.random.rand(N))
y = gp.sample(x)
gp.compute(x, yerr=yerr)
mu0, var0 = gp.predict(y, [0.0], return_var=True)
mu, var = gp.predict(y, [0.0, 1.0], return_var=True)
_, cov = gp.predict(y, [0.0, 1.0])
assert np.allclose(mu0, mu[0])
assert np.allclose(var0, var[0])
assert np.allclose(var0, cov[0, 0])
def test_gradient(solver, white_noise, seed=123, N=305, ndim=3, eps=1.32e-3):
np.random.seed(seed)
# Set up the solver.
kernel = 1.0 * kernels.ExpSquaredKernel(0.5, ndim=ndim)
kwargs = dict()
if white_noise is not None:
kwargs = dict(white_noise=white_noise, fit_white_noise=True)
if solver == HODLRSolver:
kwargs["tol"] = 1e-8
gp = GP(kernel, solver=solver, **kwargs)
# Sample some data.
x = np.random.rand(N, ndim)
x = x[np.argsort(x[:, 0])]
y = gp.sample(x)
gp.compute(x, yerr=0.1)
# Compute the initial gradient.
grad0 = gp.grad_log_likelihood(y)
vector = gp.get_parameter_vector()
for i, v in enumerate(vector):
# Compute the centered finite difference approximation to the gradient.
vector[i] = v + eps
gp.set_parameter_vector(vector)
lp = gp.lnlikelihood(y)
vector[i] = v - eps
gp.set_parameter_vector(vector)
lm = gp.lnlikelihood(y)
vector[i] = v
gp.set_parameter_vector(vector)
grad = 0.5 * (lp - lm) / eps
assert np.abs(grad - grad0[i]) < 5 * eps, \
"Gradient computation failed in dimension {0} ({1})\n{2}" \
.format(i, solver.__name__, np.abs(grad - grad0[i]))
def add_spots(self,QP=[5e-5,0.5,30.,28.]):
"""
This attribute add stellar variability using a Quasi-periodic Kernel
The activity is added using a george Kernel
"""
if not hasattr(self,'flux_spots'):
A = QP[0]
le = QP[1]
lp = QP[2]
P = QP[3]
from george import kernels, GP
k = A * kernels.ExpSine2Kernel(gamma=1./2/lp,log_period=np.log(P)) * \
kernels.ExpSquaredKernel(metric=le)
gp = GP(k)
self.flux_spots = 1 + gp.sample(self.time)
self.flux = self.flux * self.flux_spots
self.spots = True
class MockLC:
pb_names = "g' r' i' z'".split()
pb_centers = 1e-9 * array([470, 640, 780, 900])
npb = len(pb_names)
def __init__(self, setup: SimulationSetup, **kwargs):
self.setup = self.s = s = setup
self.t_exposure_d = Qty(kwargs.get('exptime', 60), 's').rescale('d')
self.t_baseline_d = Qty(s.t_baseline, 'h').rescale('d')
self.ldcs = s.ldcs
self.tm = QuadraticModel(klims=(0.01, 0.99), nk=512)
self.filters = "g' r' i' z'".split()
self.npb = len(self.filters)
self.k_apparent, self.p, self.a, self.b, self.i = s.orbital_parameters
self.duration_d = Qty(
duration_eccentric(self.p, self.k_apparent, self.a, self.i, 0, 0,
1), 'd')
# Contamination
# -------------
qe_be = TabulatedFilter('1024B_eXcelon', [
300, 325, 350, 400, 450, 500, 700, 800, 850, 900, 950, 1050, 1150
], [
0.0, 0.1, 0.25, 0.60, 0.85, 0.92, 0.96, 0.85, 0.70, 0.50, 0.30,
0.05, 0.0
])
qe_b = TabulatedFilter(
'2014B', [300, 350, 500, 550, 700, 800, 1000, 1050],
[0.10, 0.20, 0.90, 0.96, 0.90, 0.75, 0.11, 0.05])
qes = qe_be, qe_b, qe_be, qe_be
self.instrument = instrument = Instrument(
'MuSCAT2', (sdss_g, sdss_r, sdss_i, sdss_z), qes)
self.contaminator = SMContamination(instrument, "i'")
self.hteff = setup.hteff
self.cteff = setup.cteff
self.i_contamination = setup.c
self.k_true = setup.k_apparent / sqrt(1 - self.i_contamination)
self.contamination = self.contaminator.contamination(
self.i_contamination, self.hteff, self.cteff)
@property
def t_total_d(self):
return self.duration_d + 2 * self.t_baseline_d
@property
def duration_h(self):
return self.duration_d.rescale('h')
@property
def n_exp(self):
return int(self.t_total_d // self.t_exposure_d)
def __call__(self,
rseed=0,
ldcs=None,
wnsigma=None,
rnsigma=None,
rntscale=0.5):
return self.create(rseed, ldcs, wnsigma, rnsigma, rntscale)
def create(self,
rseed=0,
ldcs=None,
wnsigma=None,
rnsigma=None,
rntscale=0.5,
nights=1):
ldcs = ldcs if ldcs is not None else self.ldcs
seed(rseed)
self.time = linspace(-0.5 * float(self.t_total_d),
0.5 * float(self.t_total_d), self.n_exp)
self.time = (tile(self.time, [nights, 1]) +
(self.p * arange(nights))[:, newaxis]).ravel()
self.npt = self.time.size
self.tm.set_data(self.time)
self.transit = zeros([self.npt, 4])
for i, (ldc, c) in enumerate(zip(ldcs, self.contamination)):
self.transit[:, i] = self.tm.evaluate_ps(self.k_true, ldc, 0,
self.p, self.a, self.i)
self.transit[:, i] = c + (1 - c) * self.transit[:, i]
# White noise
# -----------
if wnsigma is not None:
self.wnoise = multivariate_normal(
zeros(atleast_2d(self.transit).shape[1]),
diag(wnsigma)**2, self.npt)
else:
self.wnoise = zeros_like(self.transit)
# Red noise
# ---------
if rnsigma and with_george:
self.gp = GP(rnsigma**2 * ExpKernel(rntscale))
self.gp.compute(self.time)
self.rnoise = self.gp.sample(self.time, self.npb).T
self.rnoise -= self.rnoise.mean(0)
else:
self.rnoise = zeros_like(self.transit)
# Final light curve
# -----------------
self.time_h = Qty(self.time, 'd').rescale('h')
self.flux = self.transit + self.wnoise + self.rnoise
return self.lcdataset
@property
def lcdataset(self):
return LCDataSet([
LCData(self.time, flux, pb)
for pb, flux in zip(self.pb_names, self.flux.T)
], self.instrument)
def plot(self, figsize=(13, 4), yoffset=0.01):
fig, axs = pl.subplots(1,
3,
figsize=figsize,
sharex='all',
sharey='all')
yshift = yoffset * arange(4)
axs[0].plot(self.time_h, self.flux + yshift)
axs[1].plot(self.time_h, self.transit + yshift)
axs[2].plot(self.time_h, 1 + self.rnoise + yshift)
pl.setp(axs, xlabel='Time [h]', xlim=self.time_h[[0, -1]])
pl.setp(axs[0], ylabel='Normalised flux')
[
pl.setp(ax, title=title) for ax, title in zip(
axs, 'Transit model + noise, Transit model, Red noise'.split(
', '))
]
fig.tight_layout()
return fig, axs
def plot_color_difference(self, figsize=(13, 4)):
fig, axs = pl.subplots(2,
3,
figsize=figsize,
sharex='all',
sharey='all')
[
ax.plot(self.time_h, 100 * (fl - self.transit[:, -1]))
for ax, fl in zip(axs[0], self.transit[:, :-1].T)
]
[
ax.plot(self.time_h, 100 * (fl - self.flux[:, -1]))
for ax, fl in zip(axs[1], self.flux[:, :-1].T)
]
[
pl.setp(ax, title='F$_{}$ - F$_z$'.format(pb))
for ax, pb in zip(axs[0], self.pb_names[:-1])
]
pl.setp(axs[:, 0], ylabel='$\Delta F$ [%]')
pl.setp(axs[1, :], xlabel='Time [h]')
pl.setp(axs, xlim=self.time_h[[0, -1]])
fig.tight_layout()
return fig
class MockLC:
pb_names = 'g r i z'.split()
pb_centers = 1e-9 * array([470, 640, 780, 900])
npb = len(pb_names)
def __init__(self, planet_name='wasp-80b', **kwargs):
self.t_exposure_d = Qty(kwargs.get('exptime', 60), 's').rescale('d')
self.t_baseline_d = Qty(kwargs.get('bltime', 0.5), 'h').rescale('d')
self.ldcs = kwargs.get(
'ldcs',
array([[0.80, 0.02], [0.61, 0.16], [0.45, 0.20], [0.36, 0.20]]))
self.filters = 'g r i z'.split()
self.npb = len(self.filters)
self.planet = planet = exocat.searchPlanet(planet_name)
self.star = star = planet.star
self.p = kwargs.get('p', None) or float(planet.P)
self.k = kwargs.get('k', None) or float(
planet.R.rescale('R_s') / star.R)
self.a = kwargs.get('a', None) or float(
planet.getParam('semimajoraxis').rescale('R_s') / star.R)
self.i = float(planet.getParam('inclination').rescale('rad'))
self.b = kwargs.get('b', self.a * cos(self.i))
self.i = arccos(self.b / self.a)
self.duration_d = Qty(
of.duration_eccentric_f(self.p, self.k, self.a, self.i, 0, 0, 1),
'd')
# Contamination
# -------------
qe_be = TabulatedFilter('1024B_eXcelon', [
300, 325, 350, 400, 450, 500, 700, 800, 850, 900, 950, 1050, 1150
], [
0.0, 0.1, 0.25, 0.60, 0.85, 0.92, 0.96, 0.85, 0.70, 0.50, 0.30,
0.05, 0.0
])
qe_b = TabulatedFilter(
'2014B', [300, 350, 500, 550, 700, 800, 1000, 1050],
[0.10, 0.20, 0.90, 0.96, 0.90, 0.75, 0.11, 0.05])
qes = qe_be, qe_b, qe_be, qe_be
instrument = Instrument('MuSCAT2', (sdss_g, sdss_r, sdss_i, sdss_z),
qes)
self.contaminator = SpectrumTool(instrument, "i'")
self.i_contamination = kwargs.get('i_contamination', 0.0)
self.cnteff = kwargs.get('contaminant_temperature', None) or float(
star.T)
self.k0 = self.k / np.sqrt(1 - self.i_contamination)
self.contamination = self.contaminator.contamination(
self.i_contamination, float(star.T), self.cnteff)
@property
def t_total_d(self):
return self.duration_d + 2 * self.t_baseline_d
@property
def duration_h(self):
return self.duration_d.rescale('h')
@property
def n_exp(self):
return int(self.t_total_d // self.t_exposure_d)
def __call__(self,
rseed=0,
ldcs=None,
wnsigma=None,
rnsigma=None,
rntscale=0.5):
return self.create(rseed, ldcs, wnsigma, rnsigma, rntscale)
def create(self,
rseed=0,
ldcs=None,
wnsigma=None,
rnsigma=None,
rntscale=0.5,
nights=1):
ldcs = ldcs if ldcs is not None else self.ldcs
seed(rseed)
self.time = linspace(-0.5 * float(self.t_total_d),
0.5 * float(self.t_total_d), self.n_exp)
self.time = (tile(self.time, [nights, 1]) +
(self.p * arange(nights))[:, newaxis]).ravel()
self.npt = self.time.size
self.transit = zeros([self.npt, 4])
for i, (ldc, c) in enumerate(zip(ldcs, self.contamination)):
self.transit[:, i] = MA().evaluate(self.time,
self.k0,
ldc,
0,
self.p,
self.a,
self.i,
c=c)
# White noise
# -----------
if wnsigma is not None:
self.wnoise = multivariate_normal(
zeros(atleast_2d(self.transit).shape[1]),
diag(wnsigma)**2, self.npt)
else:
self.wnoise = zeros_like(self.transit)
# Red noise
# ---------
if rnsigma and with_george:
self.gp = GP(rnsigma**2 * ExpKernel(rntscale))
self.gp.compute(self.time)
self.rnoise = self.gp.sample(self.time, self.npb).T
self.rnoise -= self.rnoise.mean(0)
else:
self.rnoise = zeros_like(self.transit)
# Final light curve
# -----------------
self.time_h = Qty(self.time, 'd').rescale('h')
self.flux = self.transit + self.wnoise + self.rnoise
return self.time_h, self.flux
def plot(self, figsize=(13, 4)):
fig, axs = pl.subplots(1, 3, figsize=figsize, sharex=True, sharey=True)
yshift = 0.01 * arange(4)
axs[0].plot(self.time_h, self.flux + yshift)
axs[1].plot(self.time_h, self.transit + yshift)
axs[2].plot(self.time_h, 1 + self.rnoise + yshift)
pl.setp(axs, xlabel='Time [h]', xlim=self.time_h[[0, -1]])
pl.setp(axs[0], ylabel='Normalised flux')
[
pl.setp(ax, title=title) for ax, title in zip(
axs, 'Transit model + noise, Transit model, Red noise'.split(
', '))
]
fig.tight_layout()
return fig, axs
def plot_color_difference(self, figsize=(13, 4)):
fig, axs = pl.subplots(2, 3, figsize=figsize, sharex=True, sharey=True)
[
ax.plot(self.time_h, 100 * (fl - self.transit[:, -1]))
for ax, fl in zip(axs[0], self.transit[:, :-1].T)
]
[
ax.plot(self.time_h, 100 * (fl - self.flux[:, -1]))
for ax, fl in zip(axs[1], self.flux[:, :-1].T)
]
[
pl.setp(ax, title='F$_{}$ - F$_z$'.format(pb))
for ax, pb in zip(axs[0], self.pb_names[:-1])
]
pl.setp(axs[:, 0], ylabel='$\Delta F$ [%]')
pl.setp(axs[1, :], xlabel='Time [h]')
pl.setp(axs, xlim=self.time_h[[0, -1]])
fig.tight_layout()
return fig