def optimize_hyperpars(self, n=None, **kwargs):
if n is None:
n = len(self.time)
gp = GaussianProcess(self.hyperpars)
flag, hyperpars = gp.optimize(self.time[:n], self.ferr[:n],
self.flux[:n]-1, **kwargs)
self.hyperpars = hyperpars
return flag, hyperpars
def gp(self):
if self._gp is None:
self._gp = GaussianProcess(ExpSquaredKernel(*self.hyperpars))
if not self._gp.computed:
std = np.sqrt(self.ferr**2 + self.jitter**2)
self._gp.compute(self.time, std)
return self._gp
np.random.seed(42)
def f(x):
return x * np.sin(x)
X = 10 * np.random.rand(50)
# Observations
y = f(X).ravel()
yerr = np.ones_like(y)
x = np.atleast_2d(np.linspace(-5, 15, 1001)).T
gp = GaussianProcess([0.1, 1.0])
gp.optimize(X, y, yerr=yerr)
mu, var = gp.predict(x)
print(gp.evaluate())
std = np.sqrt(var.diagonal())
vals = np.random.multivariate_normal(mu, var, 100)
pl.plot(x, mu, "k")
pl.plot(x, vals.T, "k", alpha=0.1)
pl.plot(x, mu + std, ":r")
pl.plot(x, mu - std, ":r")
t0s = np.sort(np.max(dataset.time) * np.random.rand(N))
depths = 2e-5 + (2e-4 - 2e-5) * np.random.rand(N)
durations = 0.3 + 0.2 * np.random.rand(N)
datasets = []
for t0, depth, duration in zip(t0s, depths, durations):
ds = deepcopy(dataset)
model = np.ones_like(ds.time)
model[(ds.time < t0+duration)*(ds.time > t0-duration)] *= 1.0 - depth
ds.flux *= model
datasets.append(ds)
[pl.plot(ds.time, ds.flux, ".") for ds in datasets]
pl.savefig("data.png")
# Compute the Gaussian processes on the dataset.
gp = GaussianProcess([1e-3, 3.0, 10.])
gp.compute(dataset.time, dataset.ferr)
# Loop over true epochs.
d = 0.2
correct = []
incorrect = []
for t0, depth, duration, data in zip(t0s, depths, durations, datasets):
null = gp.lnlikelihood(data.flux - 1.0)
# Compute the correct model.
model = np.ones_like(data.time)
model[(data.time < t0+duration)*(data.time > t0-duration)] *= 1.0 - 0.0001
correct.append(gp.lnlikelihood(data.flux - model) - null)
for i, t in enumerate(data.time):
np.random.seed(42)
def f(x):
return x * np.sin(x)
X = 10 * np.random.rand(50)
# Observations
y = f(X).ravel()
yerr = np.ones_like(y)
x = np.atleast_2d(np.linspace(-5, 15, 1001)).T
gp = GaussianProcess([0.1, 1.0])
gp.optimize(X, y, yerr=yerr)
mu, var = gp.predict(x)
print(gp.evaluate())
std = np.sqrt(var.diagonal())
vals = np.random.multivariate_normal(mu, var, 100)
pl.plot(x, mu, "k")
pl.plot(x, vals.T, "k", alpha=0.1)
pl.plot(x, mu + std, ":r")
pl.plot(x, mu - std, ":r")
class GPLightCurve(LightCurve):
"""
An extension to :class:`LightCurve` with a Gaussian Process likelihood
function. This does various nice things like masking NaNs and Infs and
normalizing the fluxes by the median.
:param time:
The time series in days.
:param flux:
The flux measurements in arbitrary units.
:param ferr:
The error bars on ``flux``.
:param hyperpars:
The parameters for the ``GaussianProcess`` kernel.
:param texp: (optional)
The integration time (in seconds). (default: 1626.0… Kepler
long-cadence)
:param K: (optional)
The number of bins to use in the approximate exposure time integral.
(default: 3)
"""
def __init__(self, time, flux, ferr, hyperpars, jitter=0.0, **kwargs):
if GaussianProcess is None:
raise ImportError("You need to install george to use GPs")
super(GPLightCurve, self).__init__(time, flux, ferr, **kwargs)
self._hyperpars = hyperpars
self._gp = None
self._jitter = jitter
def __getstate__(self):
return dict([(k, v) for k, v in self.__dict__.items() if k != "_gp"])
def __setstate__(self, d):
for k, v in d.items():
setattr(self, k, v)
self._gp = None
@property
def gp(self):
if self._gp is None:
self._gp = GaussianProcess(ExpSquaredKernel(*self.hyperpars))
if not self._gp.computed:
std = np.sqrt(self.ferr**2 + self.jitter**2)
self._gp.compute(self.time, std)
return self._gp
@property
def jitter(self):
return self._jitter
@jitter.setter
def jitter(self, value):
self._gp = None
self._jitter = value
@property
def hyperpars(self):
return self._hyperpars
@hyperpars.setter
def hyperpars(self, value):
self._hyperpars = value
self._gp = None
# Helper functions for the individual hyperparameters.
@property
def alpha(self):
return self._hyperpars[0]
@alpha.setter
def alpha(self, value):
h = self._hyperpars
h[0] = value
self.hyperpars = h
@property
def scale(self):
return self._hyperpars[1]
@scale.setter
def scale(self, value):
h = self._hyperpars
h[1] = value
self.hyperpars = h
def optimize_hyperpars(self, n=None, **kwargs):
if n is None:
n = len(self.time)
gp = GaussianProcess(self.hyperpars)
flag, hyperpars = gp.optimize(self.time[:n], self.ferr[:n],
self.flux[:n]-1, **kwargs)
self.hyperpars = hyperpars
return flag, hyperpars
def lnlike(self, lc):
"""
Get the likelihood of this dataset given a particular :class:`Model`.
:param model:
The predicted light curve model evaluated at ``eval_time``.
"""
return self.gp.lnlikelihood(self.flux - lc)
def predict(self, lc, size=None, resample=None):
"""
Generate a sample from the light curve probability function for a
particular :class:`Model`.
:param model:
The predicted light curve model evaluated at ``eval_time``.
"""
if resample is None:
mu, cov = self.gp.predict(self.flux - lc, self.time)
return mu + lc
t = self.time[::resample]
mu, cov = self.gp.predict(self.flux - lc, t)
mu += lc[::resample]
return np.interp(self.time, t, mu)
pl.plot(data.time, data.flux, ".")
pl.savefig("data.png")
t = data.time
f = data.flux
d = 0.2
x = np.linspace(-6, 0, 10)
y = np.linspace(-1.0, 10, 12)
s2n = np.zeros((len(x), len(y)))
ll = np.zeros((len(x), len(y)))
delta_ll = np.zeros((len(x), len(y)))
for ix, a in enumerate(x):
for iy, l in enumerate(y):
gp = GaussianProcess([10 ** a, 10 ** l, 1e6])
gp.compute(data.time, data.ferr)
null = gp.lnlikelihood(f - 1.0)
results = []
for i, t0 in enumerate(t):
if np.abs(t0 - truth[2]) < 2*d:
continue
model = np.ones_like(f)
model[(t < t0+d) * (t > t0-d)] *= 1.0 - 0.0001
results.append((t0, gp.lnlikelihood(f - model)))
results = np.array(results)
model = np.ones_like(f)
model[(t < truth[2]+d) * (t > truth[2]-d)] *= 1.0 - 0.0001
ll_true = gp.lnlikelihood(f - model)
# -*- coding: utf-8 -*- from __future__ import division, print_function, absolute_import, unicode_literals __all__ = [] import time import numpy as np import matplotlib.pyplot as pl from george import GaussianProcess import bart from bart.data import GPLightCurve # Generate fake data. gp = GaussianProcess([5e-4, 20.0, 25.0]) t = np.arange(100, 120, 0.5 / 24.0) yerr = 1e-4 * np.ones_like(t) y = gp.sample_prior(t)[0] + yerr * np.random.randn(len(yerr)) + 1 # Inject a transit. t0_true = 110.0 planet = bart.Planet(r=0.02, period=400.0, t0=t0_true) star = bart.Star(ldp=bart.ld.QuadraticLimbDarkening(0.3, 0.1)) ps = bart.PlanetarySystem(star) ps.add_planet(planet) model = ps.light_curve(t) y *= model # Plot the data. pl.plot(t, y, ".k")
from matplotlib import pyplot as pl
from george import GaussianProcess
np.random.seed(42)
def f(x):
return np.exp(-0.5 * (x[:, 0]**2 + x[:, 1]**2 / 0.1))
x = np.random.randn(200).reshape([100, 2])
y = f(x)
yerr = 0.01 * np.ones_like(y)
gp = GaussianProcess([0.1, 1.0, 1.0])
gp.optimize(x, y, yerr=yerr)
print(gp.pars)
# Grid.
X, Y = np.meshgrid(np.linspace(-3, 3, 40), np.linspace(-3, 3, 40))
mu, var = gp.predict(np.vstack([X.ravel(), Y.ravel()]).T)
ymin, ymax = y.min(), y.max()
colors = (y - ymin) / ymax
pl.figure(figsize=[4, 4])
samples = np.random.multivariate_normal(mu, var, 100)
for i in range(samples.shape[0]):
pl.clf()
pl.imshow((samples[i].reshape([40, 40]) - ymin) / ymax,
import os import sys d = os.path.dirname sys.path.insert(0, d(d(os.path.abspath(__file__)))) import numpy as np import matplotlib.pyplot as pl from george import GaussianProcess from george.kernels import ExpSquaredKernel, CosineKernel np.random.seed(123) kernel = ExpSquaredKernel(1.0, 2.3) gp = GaussianProcess(kernel) # Generate some fake data. period = 0.956 x = 10 * np.sort(np.random.rand(75)) yerr = 0.1 + 0.1 * np.random.rand(len(x)) y = gp.sample_prior(x) y += 0.8 * np.cos(2 * np.pi * x / period) y += yerr * np.random.randn(len(yerr)) # Set up a periodic kernel. pk = ExpSquaredKernel(np.sqrt(0.8), 1000.0) * CosineKernel(period) kernel2 = kernel + pk gp2 = GaussianProcess(kernel2) # Condition on this data.
from george import GaussianProcess
np.random.seed(42)
def f(x):
return np.exp(-0.5 * (x[:, 0] ** 2 + x[:, 1] ** 2 / 0.1))
x = np.random.randn(200).reshape([100, 2])
y = f(x)
yerr = 0.01 * np.ones_like(y)
gp = GaussianProcess([0.1, 1.0, 1.0])
gp.optimize(x, y, yerr=yerr)
print(gp.pars)
# Grid.
X, Y = np.meshgrid(np.linspace(-3, 3, 40), np.linspace(-3, 3, 40))
mu, var = gp.predict(np.vstack([X.ravel(), Y.ravel()]).T)
ymin, ymax = y.min(), y.max()
colors = (y - ymin) / ymax
pl.figure(figsize=[4, 4])
samples = np.random.multivariate_normal(mu, var, 100)
for i in range(samples.shape[0]):
pl.clf()
pl.imshow((samples[i].reshape([40, 40]) - ymin) / ymax,