def _general_metric(metric, N=100, ndim=3):
kernel = 0.1 * kernels.ExpSquaredKernel(metric, ndim=ndim)
x = np.random.rand(N, ndim)
M0 = kernel.get_value(x)
gp = GP(kernel)
M1 = gp.get_matrix(x)
assert np.allclose(M0, M1)
# Compute the expected matrix.
M2 = np.empty((N, N))
for i in range(N):
for j in range(N):
r = x[i] - x[j]
r2 = np.dot(r, np.linalg.solve(metric, r))
M2[i, j] = 0.1 * np.exp(-0.5 * r2)
if not np.allclose(M0, M2):
print(M0)
print()
print(M2)
print()
print(M0 - M2)
print()
print(M0 / M2)
L = np.linalg.cholesky(metric)
i = N - 1
j = N - 2
r = x[j] - x[i]
print(x[i], x[j])
print("r = ", r)
print("L.r = ", np.dot(L, r))
assert np.allclose(M0, M2)
def test_gp_mean(N=50, seed=1234):
np.random.seed(seed)
x = np.random.uniform(0, 5)
y = 5 + np.sin(x)
gp = GP(10. * kernels.ExpSquaredKernel(1.3), mean=5.0, fit_mean=True)
gp.compute(x)
check_gradient(gp, y)
def _general_metric(metric, N=100, ndim=3):
kernel = 0.1 * kernels.ExpSquaredKernel(metric, ndim=ndim)
x = np.random.rand(N, ndim)
M0 = kernel.get_value(x)
gp = GP(kernel)
M1 = gp.get_matrix(x)
assert np.allclose(M0, M1)
# Compute the expected matrix.
M2 = np.empty((N, N))
for i in range(N):
for j in range(N):
r = x[i] - x[j]
r2 = np.dot(r, np.linalg.solve(metric, r))
M2[i, j] = 0.1 * np.exp(-0.5*r2)
if not np.allclose(M0, M2):
print(M0)
print()
print(M2)
print()
print(M0 - M2)
print()
print(M0 / M2)
L = np.linalg.cholesky(metric)
i = N - 1
j = N - 2
r = x[j] - x[i]
print(x[i], x[j])
print("r = ", r)
print("L.r = ", np.dot(L, r))
assert np.allclose(M0, M2)
def test_dtype(seed=123):
np.random.seed(seed)
kernel = 0.1 * kernels.ExpSquaredKernel(1.5)
kernel.pars = [1, 2]
gp = GP(kernel)
x = np.random.rand(100)
gp.compute(x, 1e-2)
def test_dtype(seed=123):
np.random.seed(seed)
kernel = 0.1 * kernels.ExpSquaredKernel(1.5)
kernel.pars = [1, 2]
gp = GP(kernel)
x = np.random.rand(100)
gp.compute(x, 1e-2)
def __init__(self,
data=None,
param={},
bounds={},
fixed=[],
group=None,
**kwargs):
"""
:param data:
:param param:
:param bounds:
:param group:
"""
self.data = []
self.param, self.param_name, self.param_bounds = np.array(
[]), np.array([]), []
self.Ndata = 0
self.index_param_indiv = []
self.index_bounds_indiv = []
self.index_param_common = []
self.index_bounds_common = []
self.group_indiv = []
self.fixed = []
self.group_common = []
self.detrendvar = {}
self._varind = 0
self.gp = GP(solver=BasicSolver)
self._mcmc_parinit_optimized = False
self.add_data(data, param, bounds, fixed, group, **kwargs)
def test_gp_callable_mean(N=50, seed=1234):
np.random.seed(seed)
x = np.random.uniform(0, 5)
y = 5 + np.sin(x)
mean = CallableModel(lambda x: 5.0 * x)
gp = GP(10. * kernels.ExpSquaredKernel(1.3), mean=mean)
gp.compute(x)
check_gradient(gp, y)
def plotsample_QP(p, t, y, tsel, ysel):
kern, sig = kern_QP(p)
gp = GP(kern)
yerr = np.ones(len(ysel)) * sig
gp.compute(tsel, yerr)
mu = gp.sample_conditional(ysel, t)
pl.plot(t, mu, color='c', alpha=0.3)
return
def test_gp_mean(N=50, seed=1234):
np.random.seed(seed)
x = np.random.uniform(0, 5)
y = 5 + np.sin(x)
gp = GP(10. * kernels.ExpSquaredKernel(1.3),
mean=5.0, fit_mean=True)
gp.compute(x)
check_gradient(gp, y)
def test_gp_callable_mean(N=50, seed=1234):
np.random.seed(seed)
x = np.random.uniform(0, 5)
y = 5 + np.sin(x)
mean = CallableModel(lambda x: 5.0*x)
gp = GP(10. * kernels.ExpSquaredKernel(1.3), mean=mean)
gp.compute(x)
check_gradient(gp, y)
class GeorgeGP(object):
def __init__(self, kernel):
self.kernel = kernel
self._gp = GP(kernel._k)
self._y = None ## Cached inputs
self._x = None ## Cached values
self._dirty = True ## Flag telling if the arrays are up to date
@property
def is_dirty(self):
return self._dirty
def set_dirty(self, is_dirty=True):
self._dirty = is_dirty
def set_pv(self, pv=None):
if pv is not None and not array_equal(pv, self.kernel._pv):
self.kernel.set_pv(pv)
self._gp.kernel = self.kernel._k
self.set_dirty()
def set_inputs(self, x=None):
if x is not None and not array_equal(x, self._x):
self._x = x
self.set_dirty()
def _covariance_matrix(self, x1, x2=None, pv=None, separate=False):
self.set_pv(pv)
if separate:
return (self.kernel._k1.value(x1, x2),
self.kernel._k2.value(x1, x2))
else:
return self.kernel._k.value(x1, x2)
def compute(self, x=None, pv=None):
self.set_pv(pv)
self.set_inputs(x)
if self.is_dirty:
self._gp.compute(self._x, yerr=self.kernel._pm[-1], sort=False)
self.set_dirty(False)
def negll(self, pv, y=None):
y = y if y is not None else self._y
self.compute(self._x, pv)
return -self._gp.lnlikelihood(y)
def predict(self, x, mean_only=True):
return self._gp.predict(self._y, x, mean_only=mean_only)
def predict_components(self, pv, y, x1, x2=None):
self.compute(x1, pv)
b = self._gp.solver.apply_inverse(y)
K1 = self.kernel._k1.value(x1, x2)
K2 = self.kernel._k2.value(x1, x2)
mu_time = dot(K1,b)
mu_pos = dot(K2,b)
return mu_time, mu_pos
class GeorgeGP(object):
def __init__(self, kernel):
self.kernel = kernel
self._gp = GP(kernel._k)
self._y = None ## Cached inputs
self._x = None ## Cached values
self._dirty = True ## Flag telling if the arrays are up to date
@property
def is_dirty(self):
return self._dirty
def set_dirty(self, is_dirty=True):
self._dirty = is_dirty
def set_pv(self, pv=None):
if pv is not None and not array_equal(pv, self.kernel._pv):
self.kernel.set_pv(pv)
self._gp.kernel = self.kernel._k
self.set_dirty()
def set_inputs(self, x=None):
if x is not None and not array_equal(x, self._x):
self._x = x
self.set_dirty()
def _covariance_matrix(self, x1, x2=None, pv=None, separate=False):
self.set_pv(pv)
if separate:
return (self.kernel._k1.value(x1,
x2), self.kernel._k2.value(x1, x2))
else:
return self.kernel._k.value(x1, x2)
def compute(self, x=None, pv=None):
self.set_pv(pv)
self.set_inputs(x)
if self.is_dirty:
self._gp.compute(self._x, yerr=self.kernel._pm[-1], sort=False)
self.set_dirty(False)
def negll(self, pv, y=None):
y = y if y is not None else self._y
self.compute(self._x, pv)
return -self._gp.lnlikelihood(y)
def predict(self, x, mean_only=True):
return self._gp.predict(self._y, x, mean_only=mean_only)
def predict_components(self, pv, y, x1, x2=None):
self.compute(x1, pv)
b = self._gp.solver.apply_inverse(y)
K1 = self.kernel._k1.value(x1, x2)
K2 = self.kernel._k2.value(x1, x2)
mu_time = dot(K1, b)
mu_pos = dot(K2, b)
return mu_time, mu_pos
def lnprior(self, pars):
theta = pars[:self.Nbins]
if np.any(theta < 0):
return -np.inf
a, tau, err = np.exp(pars[self.Nbins:-1])
mean = pars[-1]
kernel = a * kernels.ExpSquaredKernel(tau)
gp = GP(kernel, mean=mean)
gp.compute(self.bin_centers, yerr=err)
return gp.lnlikelihood(theta) / self.smoothing
def create_gp(params):
# GP parameters
s2 = np.exp(params["log_s2"])
taux = np.exp(params["log_taux"])
tauy = np.exp(params["log_tauy"])
gpx = GP(s2 * ExpSquaredKernel(taux))
gpy = GP(s2 * ExpSquaredKernel(tauy))
return gpx, gpy
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_gp_callable_white_noise(N=50, seed=1234):
np.random.seed(seed)
x = np.random.uniform(0, 5)
y = 5 + np.sin(x)
gp = GP(10. * kernels.ExpSquaredKernel(1.3), mean=5.0,
white_noise=LinearWhiteNoise(-6, 0.01),
fit_white_noise=True)
gp.compute(x)
check_gradient(gp, y)
gp.freeze_parameter("white_noise:m")
check_gradient(gp, y)
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 test_bounds():
kernel = 10 * kernels.ExpSquaredKernel(1.0, metric_bounds=[(None, 4.0)])
kernel += 0.5 * kernels.RationalQuadraticKernel(log_alpha=0.1, metric=5.0)
gp = GP(kernel, white_noise=LinearWhiteNoise(1.0, 0.1))
# Test bounds length.
assert len(gp.get_parameter_bounds()) == len(gp.get_parameter_vector())
gp.freeze_all_parameters()
gp.thaw_parameter("white_noise:m")
assert len(gp.get_parameter_bounds()) == len(gp.get_parameter_vector())
# Test invalid bounds specification.
with pytest.raises(ValueError):
kernels.ExpSine2Kernel(gamma=0.1, log_period=5.0, bounds=[10.0])
def lnprior(self, pars):
"""
Smoothing prior using gaussian process.
We will learn the hyperparameters and marginalize over them.
"""
theta = pars[:self.Nbins]
if np.any(theta < 0):
return -np.inf
a, tau, err = np.exp(pars[self.Nbins:-1])
mean = pars[-1]
kernel = a * kernels.ExpSquaredKernel(tau)
gp = GP(kernel, mean=mean)
gp.compute(self.bin_centers, yerr=err)
return gp.lnlikelihood(theta) / self.smoothing
def test_axis_algined_metric(seed=1234, N=100, ndim=3):
np.random.seed(seed)
kernel = 0.1 * kernels.ExpSquaredKernel(np.ones(ndim), ndim=ndim)
x = np.random.rand(N, ndim)
M0 = kernel.get_value(x)
gp = GP(kernel)
M1 = gp.get_matrix(x)
assert np.allclose(M0, M1)
# Compute the expected matrix.
M2 = 0.1*np.exp(-0.5*np.sum((x[None, :, :] - x[:, None, :])**2, axis=-1))
assert np.allclose(M0, M2)
def test_axis_algined_metric(seed=1234, N=100, ndim=3):
np.random.seed(seed)
kernel = 0.1 * kernels.ExpSquaredKernel(np.ones(ndim), ndim=ndim)
x = np.random.rand(N, ndim)
M0 = kernel.get_value(x)
gp = GP(kernel)
M1 = gp.get_matrix(x)
assert np.allclose(M0, M1)
# Compute the expected matrix.
M2 = 0.1 * np.exp(-0.5 * np.sum(
(x[None, :, :] - x[:, None, :])**2, axis=-1))
assert np.allclose(M0, M2)
def test_bounds():
kernel = 10 * kernels.ExpSquaredKernel(1.0, metric_bounds=[(None, 4.0)])
kernel += 0.5 * kernels.RationalQuadraticKernel(log_alpha=0.1, metric=5.0)
gp = GP(kernel, white_noise=LinearWhiteNoise(1.0, 0.1))
# Test bounds length.
assert len(gp.get_parameter_bounds()) == len(gp.get_parameter_vector())
gp.freeze_all_parameters()
gp.thaw_parameter("white_noise:m")
assert len(gp.get_parameter_bounds()) == len(gp.get_parameter_vector())
# Test invalid bounds specification.
with pytest.raises(ValueError):
kernels.ExpSine2Kernel(gamma=0.1, log_period=5.0, bounds=[10.0])
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
def test_pickle(solver, success, N=50, seed=123):
np.random.seed(seed)
kernel = 0.1 * kernels.ExpSquaredKernel(1.5)
kernel.pars = [1, 2]
gp = GP(kernel, solver=solver)
x = np.random.rand(100)
gp.compute(x, 1e-2)
s = pickle.dumps(gp, -1)
gp = pickle.loads(s)
if success:
gp.compute = _fake_compute
gp.lnlikelihood(np.sin(x))
def plotpred_QP(p, t, y):
kern, sig = kern_QP(p)
gp = GP(kern)
yerr = np.ones(len(y)) * sig
gp.compute(t, yerr)
mu, cov = gp.predict(y, t)
sigma = np.diag(cov)
sigma = np.sqrt(sigma**2 + yerr**2)
pl.fill_between(t, mu + 2 * sigma, mu - 2 * sigma, \
color='c', alpha=0.3)
pl.plot(t, mu, color='c', lw=2)
nper = (len(p) - 1) / 4
# if nper > 1:
# cols = ['c','m','y','k']
# for i in range(nper):
# p1 = np.append(p[i*4:i*4+4], p[-1])
# k1, sig = kern_QP(p1)
# b = gp.solver.apply_inverse(y)
# X = np.transpose([t])
# K1 = k1.value(t, t)
# mu1 = np.dot(K1, b)
# col = np.roll(cols, -i)[0]
# pl.plot(t, mu, color = col, lw = 2)
return
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_gp_callable_white_noise(N=50, seed=1234):
np.random.seed(seed)
x = np.random.uniform(0, 5)
y = 5 + np.sin(x)
gp = GP(10. * kernels.ExpSquaredKernel(1.3),
mean=5.0,
white_noise=LinearWhiteNoise(-6, 0.01),
fit_white_noise=True)
gp.compute(x)
check_gradient(gp, y)
gp.freeze_parameter("white_noise:m")
check_gradient(gp, y)
def test_pickle(solver, success, N=50, seed=123):
np.random.seed(seed)
kernel = 0.1 * kernels.ExpSquaredKernel(1.5)
kernel.pars = [1, 2]
gp = GP(kernel, solver=solver)
x = np.random.rand(100)
gp.compute(x, 1e-2)
s = pickle.dumps(gp, -1)
gp = pickle.loads(s)
if success:
gp.compute = _fake_compute
gp.lnlikelihood(np.sin(x))
def __init__(self, mean, covariance, points, lnlikes, quiet=True):
self.mean = mean
self.cov = covariance
#Let's try only interpolating over points that are
#better than, say, 10-ish sigma
dof = len(self.mean)
inds = np.fabs(np.max(lnlikes) - lnlikes) < 100 * dof
print(inds)
print(lnlikes)
self.points = points[inds]
self.lnlikes_true = lnlikes[inds]
self.lnlike_max = np.max(lnlikes[inds])
self.lnlikes = lnlikes[inds] - self.lnlike_max #max is now at 0
self.x = self._transform_data(self.points)
print(max(self.lnlikes), min(self.lnlikes))
_guess = 4.5 #kernel length guess
kernel = kernels.ExpSquaredKernel(metric=_guess, ndim=dof)
lnPmin = np.min(self.lnlikes)
gp = GP(kernel, mean=lnPmin - np.fabs(lnPmin * 3))
gp.compute(self.x)
def neg_ln_likelihood(p):
gp.set_parameter_vector(p)
return -gp.log_likelihood(self.lnlikes)
def grad_neg_ln_likelihood(p):
gp.set_parameter_vector(p)
return -gp.grad_log_likelihood(self.lnlikes)
result = minimize(neg_ln_likelihood,
gp.get_parameter_vector(),
jac=grad_neg_ln_likelihood)
if not quiet:
print(result)
gp.set_parameter_vector(result.x)
self.gp = gp
def __init__(self, target, datasets, filters, model='pb_independent_k', fit_wn=True, **kwargs):
super().__init__(target, datasets, filters, model, **kwargs)
pbl = [LParameter('bl_{:d}'.format(i), 'baseline', '', N(1, 1e-2), bounds=(-inf,inf)) for i in range(self.nlc)]
self.ps.thaw()
self.ps.add_lightcurve_block('baseline', 1, self.nlc, pbl)
self.ps.freeze()
self._slbl = self.ps.blocks[-1].slice
self._stbl = self.ps.blocks[-1].start
self.logwnvar = log(array(self.wn) ** 2)
self._create_kernel()
self.covariates = [cv[:, self.covids] for cv in self.covariates]
self.freeze = []
self.standardize = []
self.gps = [GP(self._create_kernel(),
mean=0., fit_mean=False,
white_noise=0.8*wn, fit_white_noise=fit_wn) for wn in self.logwnvar]
# Freeze the GP hyperparameters marked as frozen in _create_kernel
for gp in self.gps:
pars = gp.get_parameter_names()
[gp.freeze_parameter(pars[i]) for i in self.freeze]
# Standardize the covariates marked to be standardized in _create_kernel
for c in self.covariates:
for i in self.standardize:
c[:,i] = (c[:,i] - c[:,i].min()) / c[:,i].ptp()
self.compute_always = False
self.compute_gps()
self.de = None
self.gphpres = None
self.gphps = None
def test_prediction(solver, seed=42):
"""Basic sanity checks for GP regression."""
np.random.seed(seed)
kernel = kernels.ExpSquaredKernel(1.0)
kwargs = dict()
if solver == HODLRSolver:
kwargs["tol"] = 1e-8
gp = GP(kernel, solver=solver, white_noise=0.0, **kwargs)
x0 = np.linspace(-10, 10, 500)
x = np.sort(np.random.uniform(-10, 10, 300))
gp.compute(x)
y = np.sin(x)
mu, cov = gp.predict(y, x0)
Kstar = gp.get_matrix(x0, x)
K = gp.get_matrix(x)
K[np.diag_indices_from(K)] += 1.0
mu0 = np.dot(Kstar, np.linalg.solve(K, y))
print(np.abs(mu - mu0).max())
assert np.allclose(mu, mu0)
def train(self, kernel=None):
"""Train a Gaussian Process to interpolate the log-likelihood
of the training samples.
Args:
kernel (george.kernels.Kernel object): kernel to use, or any
acceptable object that can be accepted by the george.GP object
"""
inds = self.training_inds
x = self.chain_rotated_regularized[inds]
lnL = self.lnlikes[inds]
_guess = 4.5
if kernel is None:
kernel = kernels.ExpSquaredKernel(metric=_guess, ndim=len(x[0]))
#Note: the mean is set slightly lower that the minimum lnlike
lnPmin = np.min(self.lnlikes)
gp = GP(kernel, mean=lnPmin - np.fabs(lnPmin * 3))
gp.compute(x)
def neg_ln_likelihood(p):
gp.set_parameter_vector(p)
return -gp.log_likelihood(lnL)
def grad_neg_ln_likelihood(p):
gp.set_parameter_vector(p)
return -gp.grad_log_likelihood(lnL)
result = minimize(neg_ln_likelihood,
gp.get_parameter_vector(),
jac=grad_neg_ln_likelihood)
print(result)
gp.set_parameter_vector(result.x)
self.gp = gp
self.lnL_training = lnL
return
def test_repeated_prediction_cache():
kernel = kernels.ExpSquaredKernel(1.0)
gp = GP(kernel)
x = np.array((-1, 0, 1))
gp.compute(x)
t = np.array((-.5, .3, 1.2))
y = x / x.std()
mu0, mu1 = (gp.predict(y, t, return_cov=False) for _ in range(2))
assert np.array_equal(mu0, mu1), \
"Identical training data must give identical predictions " \
"(problem with GP cache)."
y2 = 2 * y
mu2 = gp.predict(y2, t, return_cov=False)
assert not np.array_equal(mu0, mu2), \
"Different training data must give different predictions " \
"(problem with GP cache)."
a0 = gp._alpha
gp.kernel[0] += 0.1
gp.recompute()
gp._compute_alpha(y2, True)
a1 = gp._alpha
assert not np.allclose(a0, a1), \
"Different kernel parameters must give different alphas " \
"(problem with GP cache)."
mu, cov = gp.predict(y2, t)
_, var = gp.predict(y2, t, return_var=True)
assert np.allclose(np.diag(cov), var), \
"The predictive variance must be equal to the diagonal of the " \
"predictive covariance."
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 get_linear_gp(pars):
amp, sigma = pars
kernel = (amp * PolynomialKernel(sigma, order=2))
return GP(kernel)
def get_composite_gp(pars):
amp, sigma, amp2, length = pars
kernel = (amp * PolynomialKernel(sigma, order=1) +
amp2 * ExpSquaredKernel(length))
return GP(kernel)
def test_parameters():
kernel = 10 * kernels.ExpSquaredKernel(1.0)
kernel += 0.5 * kernels.RationalQuadraticKernel(log_alpha=0.1, metric=5.0)
gp = GP(kernel, white_noise=LinearWhiteNoise(1.0, 0.1))
n = len(gp.get_parameter_vector())
assert n == len(gp.get_parameter_names())
assert n - 2 == len(kernel.get_parameter_names())
gp.freeze_parameter(gp.get_parameter_names()[0])
assert n - 1 == len(gp.get_parameter_names())
assert n - 1 == len(gp.get_parameter_vector())
gp.freeze_all_parameters()
assert len(gp.get_parameter_names()) == 0
assert len(gp.get_parameter_vector()) == 0
gp.kernel.thaw_all_parameters()
gp.white_noise.thaw_all_parameters()
assert n == len(gp.get_parameter_vector())
assert n == len(gp.get_parameter_names())
assert np.allclose(kernel[0], np.log(10.))
def get_fancy_gp(pars):
amp, a, b, c, d = pars
kernel = amp * MyDijetKernelSimp(a, b, c, d)
return GP(kernel)
def __init__(self, kernel):
self.kernel = kernel
self._gp = GP(kernel._k)
self._y = None ## Cached inputs
self._x = None ## Cached values
self._dirty = True ## Flag telling if the arrays are up to date
def run(self):
gp = GP(self._kernel)
gp.compute(self._x)
y = self._y
pipe = self._out_pipe
for cmd, args, kwargs in iter(pipe.recv, None):
if cmd == 'predict':
result = gp.predict(y, *args, **kwargs)
if len(result) == 2:
# only return the diagonal of the covariance matrix
result = result[0], result[1].diagonal()
elif cmd == 'get_kernel_pars':
result = gp.kernel.pars
elif cmd == 'set_kernel_pars':
gp.kernel.pars = args[0]
result = None
elif cmd == 'train':
prior, nstarts, verbose = args
# define function for negative log-likelihood and its gradient
def nll(vector, bad_return=(1e30, np.zeros(len(gp.kernel)))):
# prevent exp overflow
if np.any(vector > 100.):
return bad_return
gp.kernel.vector = vector
ll = gp.lnlikelihood(y, quiet=True)
if not np.isfinite(ll):
return bad_return
grad = gp.grad_lnlikelihood(y, quiet=True)
return -ll, -grad
if verbose:
print(self.name, 'starting training')
# sample random initial positions from prior
# run optimization for each
result = tuple(
optimize.minimize(nll, x0, jac=True, **kwargs)
for x0 in np.log(prior.rvs(nstarts))
)
if verbose:
print(self.name, 'training complete')
# Print a table of results.
# Since results are sure to repeat,
# group them and output a row for each group:
# number ll *hyperpars
for nll, group in itertools.groupby(
sorted(result, key=lambda r: r.fun),
key=lambda r: round(r.fun, 2)
):
for n, r in enumerate(group, start=1):
pass
print(' ', n, -nll, _format_number_list(*np.exp(r.x)))
# set hyperparameters to opt result with best likelihood
gp.kernel.vector = min(result, key=lambda r: r.fun).x
else:
result = ValueError('Unknown command: {}.'.format(cmd))
pipe.send(result)
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
def lnlike(p, t, y, yerr, solver=BasicSolver):
a, tau = np.exp(p[:2])
gp = GP(a * kernels.Matern32Kernel(tau) + 0.001, solver=solver)
gp.compute(t, yerr)
return gp.lnlikelihood(y - model(p, t))
class model_transit_lightcurve(object):
per = 0
ldmethod = 'quad'
def __init__(self,
data=None,
param={},
bounds={},
fixed=[],
group=None,
**kwargs):
"""
:param data:
:param param:
:param bounds:
:param group:
"""
self.data = []
self.param, self.param_name, self.param_bounds = np.array(
[]), np.array([]), []
self.Ndata = 0
self.index_param_indiv = []
self.index_bounds_indiv = []
self.index_param_common = []
self.index_bounds_common = []
self.group_indiv = []
self.fixed = []
self.group_common = []
self.detrendvar = {}
self._varind = 0
self.gp = GP(solver=BasicSolver)
self._mcmc_parinit_optimized = False
self.add_data(data, param, bounds, fixed, group, **kwargs)
def add_data(self, data, param, bounds, fixed=[], group=None, **kwargs):
if data:
if type(data) == str:
data = np.loadtxt(data, unpack=True, **kwargs)
if self.Ndata == 0: self.data = data
if self.Ndata == 1: self.data = [self.data]
if self.Ndata > 0: self.data.append(data)
parlen = len(self.param)
bounlen = len(self.param_bounds)
if param:
if isinstance(param, dict) and type(param) != NamedParam:
param = NamedParam(param)
self.param_name = np.append(self.param_name, param.keys())
self.param = np.append(self.param,
[param[key] for key in param])
fixedkeys = [
param[fx] if type(fx) == int else fx for fx in fixed
]
self.param_bounds += [
bounds[key] for key in bounds if key not in fixedkeys
]
self.group_indiv.append(group)
self.fixed += [
(fx if type(fx) == int else list(param).index(fx)) + parlen
for fx in fixed
]
self.index_param_indiv.append(np.arange(len(param)) + parlen)
self.index_bounds_indiv.append(np.arange(len(bounds)) + bounlen)
if self.Ndata == 1: self.detrendvar = [self.detrendvar]
if self.Ndata > 0: self.detrendvar.append({})
self.Ndata += 1
def add_indiv_param(self, param, bounds, fixed=[], dataindex=-1):
if self.Ndata < 1: return
if param:
if isinstance(param, dict) and type(param) != NamedParam:
param = NamedParam(param)
parlen = len(self.param)
bounlen = len(self.param_bounds)
self.param_name = np.append(self.param_name, param.keys())
self.param = np.append(self.param, [param[key] for key in param])
fixedkeys = [param[fx] if type(fx) == int else fx for fx in fixed]
self.param_bounds += [
bounds[key] for key in bounds if key not in fixedkeys
]
self.index_param_indiv[dataindex] = np.append(
self.index_param_indiv[dataindex],
np.arange(len(param)) + parlen)
self.index_bounds_indiv[dataindex] = np.append(
self.index_bounds_indiv[dataindex],
np.arange(len(bounds)) + bounlen)
self.fixed += [parlen + fx for fx in fixed]
def add_common_param(
self,
param,
bounds={},
fixed=[],
group=None): # TODO: ignore bounds keys if fixed is not []
if self.Ndata < 1: return
if param:
if isinstance(param, dict) and type(param) != NamedParam:
param = NamedParam(param)
parlen = len(self.param)
bounlen = len(self.param_bounds)
self.param_name = np.append(self.param_name, param.keys())
self.param = np.append(self.param, [param[key] for key in param])
fixedkeys = [param[fx] if type(fx) == int else fx for fx in fixed]
self.param_bounds += [
bounds[key] for key in bounds if key not in fixedkeys
]
self.group_common.append(group)
self.fixed += [
(fx if type(fx) == int else list(param.keys()).index(fx)) +
parlen for fx in fixed
]
self.index_param_common.append(np.arange(len(param)) + parlen)
self.index_bounds_common.append(np.arange(len(bounds)) + bounlen)
def add_detrend_param(self,
variable=0,
name='',
dataindex=-1,
coeff=[],
bounds=[],
fixed=[]):
if type(variable) == int:
varnames = ['t', 'flux', 'err']
if self.Ndata == 1 and dataindex in [0, -1]:
var = self.data[variable]
elif self.Ndata > 1:
var = self.data[dataindex][variable]
if not name: name = varnames[variable]
else:
var = variable
if not name:
name = 'var' + str(self._varind)
self._varind += 1
name = 'det_' + name
if coeff:
parlen = len(self.param)
bounlen = len(self.param_bounds)
self.param = np.append(self.param, coeff)
self.param_name = np.append(
self.param_name, [name + f'_{i}' for i in range(len(coeff))])
self.param_bounds += bounds
if self.Ndata == 1 and dataindex in [0, -1]:
self.detrendvar.update({name: (var, len(coeff))})
elif self.Ndata > 1:
self.detrendvar[dataindex].update({name: (var, len(coeff))})
self.index_param_indiv[dataindex] = np.append(
self.index_param_indiv[dataindex],
np.arange(len(coeff)) + parlen)
self.index_bounds_indiv[dataindex] = np.append(
self.index_bounds_indiv[dataindex],
np.arange(len(bounds)) + bounlen)
self.fixed += [parlen + fx for fx in fixed]
def get_named_param(self, param):
if type(param) != np.ndarray: param = np.array(param)
if self.Ndata == 1:
nparam = NamedParam(
zip(self.param_name[self.index_param_indiv[0]],
param[self.index_param_indiv[0]]))
for j, icarr in enumerate(self.index_param_common):
if not self.group_indiv[0] or not self.group_common[
j] or self.group_indiv[0] == self.group_common[j]:
nparam.update(zip(self.param_name[icarr], param[icarr]))
return nparam
paramseg = [NamedParam() for _ in self.index_param_indiv]
for i, iiarr in enumerate(self.index_param_indiv):
for j, icarr in enumerate(self.index_param_common):
if not self.group_indiv[i] or not self.group_common[
j] or self.group_indiv[i] == self.group_common[j]:
paramseg[i].update(
zip(self.param_name[icarr], param[icarr]))
paramseg[i].update(zip(self.param_name[iiarr], param[iiarr]))
return paramseg
def _model_function(self, param, t, named=False, detrend=True):
if not named: param = self.get_named_param(param)
if detrend:
return direct_tfm_with_detrend(param, t, self.per, self.detrendvar,
self.ldmethod)
return direct_tfm(param, t, self.per, self.ldmethod)
@staticmethod
def _contains_gppar(param):
if isinstance(param, (dict, NamedParam)):
return 'gpa' in param and 'gptau' in param
return ['gpa' in par and 'gptau' in par for par in param]
@staticmethod
def _contais_detrendvar(detrendvar):
if isinstance(detrendvar, dict):
return len(detrendvar) == 0
return [len(dtv) == 0 for dtv in detrendvar]
def log_likelihood_gp(self, param):
if self.Ndata == 0: return
if not self._calcgp: return
nparam = self.get_named_param(param)
if self.Ndata == 1:
detfac = get_detrend_factor(
nparam, self.detrendvar) if self._calcdetrend else 1
self.gp.kernel = kernel(nparam['gpa'], nparam['gptau'])
if np.any(np.isnan(detfac)): print('detfac nan')
if np.any(np.isinf(detfac)): print('detfac inf')
if np.any(np.isnan(nparam['gpa'])): print('gpa nan')
if np.any(np.isinf(nparam['gpa'])): print('gpa inf')
if np.any(np.isnan(nparam['gptau'])): print('gptau nan')
if np.any(np.isinf(nparam['gptau'])): print('gptau inf')
if np.any(np.isnan(self.data[0])): print('t nan')
if np.any(np.isinf(self.data[0])): print('t inf')
if np.any(np.isnan(self.data[2])): print('err nan')
if np.any(np.isinf(self.data[2])): print('err inf')
try:
self.gp.compute(self.data[0], self.data[2] / detfac)
except:
print(nparam)
print(np.any(detfac == 0))
raise
return self.gp.log_likelihood(
self.data[1] / detfac - self._model_function(
nparam, self.data[0], named=True, detrend=False))
detfac = get_detrend_factor(
nparam, self.detrendvar) if self._calcdetrend else np.ones(
self.Ndata)
llhood = []
for i in range(self.Ndata):
if self._calcgp[i]:
self.gp.kernel = kernel(nparam[i]['gpa'], nparam[i]['gptau'])
self.gp.compute(self.data[i][0], self.data[i][2] / detfac[i])
llhood.append(
self.gp.log_likelihood(
self.data[i][1] / detfac[i] -
self._model_function(nparam[i],
self.data[i][0],
named=True,
detrend=False)))
else:
llhood.append(None)
return llhood
def run_mcmc(self, *args, **kwargs):
data = self.data if self.Ndata == 1 else list(
map(list, zip(*self.data)))
param = kwargs.pop('param_init', self.param)
bounds = kwargs.pop('param_bounds', self.param_bounds)
priorpdf_type = kwargs.pop('priorpdftype', 'uniform')
priorpdf_args = kwargs.pop('priorpdfargs', ())
self._calcgp = self._contains_gppar(self.get_named_param(param))
if not np.any(self._calcgp): self._calcgp = False
self._calcdetrend = self._contais_detrendvar(self.detrendvar)
if not np.any(self._calcdetrend): self._calcdetrend = False
llhood = self.log_likelihood_gp if self._calcgp else None
self.mcmc = MCMC(np.array(data),
param,
bounds,
fixpos=self.fixed,
modelfunc=self._model_function,
loglikelihood=llhood,
ignorex_loglikelihood=True,
priorpdf_type=priorpdf_type,
priorpdf_args=priorpdf_args)
self.mcmc.mcmc_name = kwargs.pop('mcmc_name', '')
self.mcmc.param_names = self.param_name_plus_group
optimize = kwargs.pop('preoptimize', False)
if optimize:
self.mcmc.optimized_initpar()
self._mcmc_parinit_optimized = True
self.mcmc(*args, **kwargs)
self.mcmc_accepted = self.mcmc.accepted
self.mcmc_nwalker = self.mcmc.Nwalker
self.mcmc_niterate = self.mcmc.Niterate
@property
def skeleton(self):
keys = [
'Ndata', 'index_param_indiv', 'index_bounds_indiv',
'index_param_common', 'index_bounds_common', 'group_indiv',
'group_common', 'fixed', 'detrendvar', 'param_name',
'param_bounds', '_varind', 'mcmc_accepted', 'mcmc_nwalker',
'mcmc_niterate'
]
skeleton = dict(input_data=self.data, param_init=self.param)
for key in keys:
try:
skeleton[key] = self.__getattribute__(key)
except:
skeleton[key] = None
skeleton['mcmc_param_init_optimized'] = self.mcmc.param_init if self._mcmc_parinit_optimized else []
return skeleton
@property
def param_name_plus_group(self):
groupexp = np.full(len(self.param), '', dtype=object)
for i in range(len(self.group_indiv)):
if self.group_indiv[i]:
groupexp[self.index_param_indiv[i]] = '-' + self.group_indiv[i]
for i in range(len(self.group_common)):
if self.group_common[i]:
groupexp[self.index_param_common[i]] = self.group_common[i]
return list(map(''.join, zip(self.param_name, groupexp)))
def saveall(self,
retrieval_skeleton='',
params_mcmc='',
mcmc_params_rawsample='',
results_optimized='',
**kwargs):
import pickle as pkl
if retrieval_skeleton:
pkl.dump(self.skeleton, open(retrieval_skeleton + '.pkl', 'wb'))
if params_mcmc:
if 'header' not in kwargs:
kwargs['header'] = '\t'.join(self.param_name_plus_group)
np.savetxt(params_mcmc, self.params_mcmc, **kwargs)
def load_retrieval_skeleton(self, skeleton='', param_init='init'):
import pickle as pkl
if skeleton:
if type(skeleton) == str and os.path.exists(skeleton + '.pkl'):
skeleton = pkl.load(open(skeleton + '.pkl', 'rb'))
self.data = skeleton.pop('input_data')
parami = skeleton.pop('param_init')
parammo = skeleton.pop('mcmc_param_init_optimized')
paramo = skeleton.pop('param_optimized', [])
if param_init == 'init': self.param = parami
if param_init == 'mcmc_preoptimized': self.param = parammo
if param_init == 'mcmc_final':
self.param = self.median_err_params_mcmc[:, 0]
if param_init == 'optimized_final': self.param = paramo
for key in skeleton:
self.__setattr__(key, skeleton[key])
def load_params_mcmc(self, source):
if source:
if type(source) == str and os.path.exists(source):
source = np.loadtxt(source)
self.params_mcmc = source
def get_flatsamples(self, saveto='', **kwargs):
self.params_mcmc = self.mcmc.get_flatsamples(**kwargs)
def load_backend_mcmc(self, source, mcmc_name=''):
if not hasattr(self, 'mcmc'):
self.mcmc = MCMC([], [])
self.mcmc.mcmc_name = mcmc_name
self.mcmc.param_names = self.param_name_plus_group
self.mcmc.load_backend(source)
self.mcmc.Niterate, self.mcmc.Nwalker, self.mcmc.Ndim = self.mcmc.get_samples(
).shape
@staticmethod
def chooseNflatten_from_sample(samples, burn=0, thin=1, accepted=[]):
return samples[burn::thin, :, :].reshape(
-1, samples.shape[2]) if len(accepted) != 0 else samples[
burn::thin, accepted, :].reshape(-1, samples.shape[2])
def get_best_fit(self, **kwargs):
data = self.data if self.Ndata == 1 else list(
map(list, zip(*self.data)))
param = kwargs.pop('param_init', self.param)
bounds = kwargs.pop('param_bounds', self.param_bounds)
self.mcmc = MCMC(np.array(data),
param,
bounds,
fixpos=self.fixed,
modelfunc=self._model_function,
loglikelihood=self.log_likelihood_gp,
ignorex_loglikelihood=True)
def get_transit_model(self,
param,
t,
named=False,
detrend=True,
denoiseGP=True):
if not named:
if np.ndim(param): param = self.get_named_param(param)
elif np.ndim(param) == 2:
param = list(param)
for i in range(len(param)):
param[i] = self.get_named_param(param[i])
modelop = self._model_function(param, t, named=True, detrend=detrend)
if not np.any(self._contains_gppar(param)) or not denoiseGP:
return modelop
if self.Ndata == 1:
self.gp.kernel = kernel(param['gpa'], param['gptau'])
self.gp.compute(self.data[0], self.data[2])
return self.gp.sample_conditional(self.data[1] - modelop,
t) + modelop
for i in range(self.Ndata):
if self._contains_gppar(param[i]):
self.gp.kernel = kernel(param[i]['gpa'], param[i]['gptau'])
self.gp.compute(self.data[i][0], self.data[i][2])
modelop[i] += self.gp.sample_conditional(self.data[i][1] -
modelop[i],
t,
size=100).mean(0)
return modelop
def get_adjusted_data(self,
param,
named=False,
detrend=True,
denoiseGP=True):
if self.Ndata == 0: return
if not named:
if np.ndim(param): param = self.get_named_param(param)
elif np.ndim(param) == 2:
param = list(param)
for i in range(len(param)):
param[i] = self.get_named_param(param[i])
if detrend and self._calcdetrend:
detfac = get_detrend_factor(param, self.detrendvar)
if self.Ndata == 1:
t, f, e = self.data
if detrend and self._calcdetrend:
f /= detfac
e /= detfac
if denoiseGP and self._calcgp:
self.gp.kernel = kernel(param['gpa'], param['gptau'])
self.gp.compute(t, e)
f -= self.gp.sample_conditional(
f -
self._model_function(param, t, named=True, detrend=False),
t,
size=100).mean(0)
return t, f, e
t, f, e = [], [], []
for i in range(self.Ndata):
ti, fi, ei = self.data[i]
if detrend and self._calcdetrend:
fi /= detfac[i]
ei /= detfac[i]
if denoiseGP and self._calcgp:
self.gp.kernel = kernel(param[i]['gpa'], param[i]['gptau'])
self.gp.compute(ti, ei)
fi -= self.gp.sample_conditional(fi - self._model_function(
param[i], ti, named=True, detrend=False),
t,
size=100).mean(0)
t.append(ti)
f.append(fi)
e.append(ei)
return t, f, e
@property
def median_err_params_mcmc(self):
return get_median_error_from_distribution(self.params_mcmc,
sigma=1,
method='percentile',
saveas='')
def save_median_err_params_mcmc(self,
saveto='',
parnames=[],
display=True):
parfinal = self.median_err_params_mcmc.T
print(parfinal.shape)
if not parnames: parnames = self.mcmc.param_names
if os.path.exists(saveto): os.remove(saveto)
for i, parname in enumerate(parnames):
if display:
print(
parname +
f': {parfinal[i, 0]} +{parfinal[i, 1]} -{parfinal[i, 2]}')
if saveto:
print(
parname +
f': {parfinal[i, 0]} +{parfinal[i, 1]} -{parfinal[i, 2]}',
file=open(saveto, 'a'))
def overplot_model_median_err_params_mcmc(self,
multifig=False,
axis='auto',
figsize=(10, 10)):
import matplotlib.pyplot as plt
params = self.median_err_params_mcmc.T
t, f, e = self.get_adjusted_data(params[:, 0])
if self.Ndata == 1:
fig, ax = plt.subplots(figsize=figsize)
midfluxfit = self.get_transit_model(params[:, 0],
t,
detrend=False,
denoiseGP=False)
ax.errorbar(t, f, e, fmt='.')
ax.plot(t,
midfluxfit,
c='r',
lw=3,
label='Model corr. to median of parameters')
return fig, ax
if not multifig:
if axis == 'auto':
figure, axes = plt.subplots(self.Ndata, 1, figsize=figsize)
elif isinstance(axis, (tuple, list)) and len(axis) == 2:
figure, axes = plt.subplots(axis[0], axis[1], figsize=figsize)
axes = np.ravel(axes)
else:
figure, axes = [], []
for i in range(self.Ndata):
if multifig:
fig, ax = plt.subplots(figsize=figsize)
figure.append(fig)
axes.append(ax)
else:
ax = axes[i]
midfluxfit = self.get_transit_model(params[i][:, 0],
t[i],
detrend=False,
denoiseGP=False)
ax.errorbar(t[i], f[i], e[i], fmt='.')
ax.plot(t[i],
midfluxfit,
c='r',
lw=3,
label='Model corr. to median of parameters')
return figure, axes
def create_gp(self):
# This function uses the kernel defined above to compute and train the Gaussian Process model
gp = GP(kernel=self.kk, mean=self.mean)
gp.compute(self.x_train, self.sigma_n)
return gp
def test_parameters():
kernel = 10 * kernels.ExpSquaredKernel(1.0)
kernel += 0.5 * kernels.RationalQuadraticKernel(log_alpha=0.1, metric=5.0)
gp = GP(kernel, white_noise=LinearWhiteNoise(1.0, 0.1))
n = len(gp.get_parameter_vector())
assert n == len(gp.get_parameter_names())
assert n - 2 == len(kernel.get_parameter_names())
gp.freeze_parameter(gp.get_parameter_names()[0])
assert n - 1 == len(gp.get_parameter_names())
assert n - 1 == len(gp.get_parameter_vector())
gp.freeze_all_parameters()
assert len(gp.get_parameter_names()) == 0
assert len(gp.get_parameter_vector()) == 0
gp.kernel.thaw_all_parameters()
gp.white_noise.thaw_all_parameters()
assert n == len(gp.get_parameter_vector())
assert n == len(gp.get_parameter_names())
assert np.allclose(kernel[0], np.log(10.))