def Fit0_Jitter(x, y, yerr = None, verbose = True, doPlot = False, \
xpred = None):
k = terms.Matern32Term(log_sigma=0.0, log_rho=0.0)
if yerr is None:
wn = np.median(abs(np.diff(y)))
else:
wn = np.median(yerr)
k += terms.JitterTerm(log_sigma=np.log(wn))
gp = GP(k, mean=1.0)
gp.compute(x)
HP_init = gp.get_parameter_vector()
soln = minimize(NLL0, gp.get_parameter_vector(), jac=True, args=(gp, y))
gp.set_parameter_vector(soln.x)
if verbose:
print 'Initial pars:', HP_init
print 'Fitted pars:', soln.x
if xpred is None:
return soln.x
mu, var = gp.predict(y, xpred, return_var=True)
std = np.sqrt(var)
if doPlot:
plt.errorbar(x, y, yerr=yerr, fmt=".k", capsize=0)
plt.plot(xpred, mu, 'C0')
plt.fill_between(xpred,
mu + std,
mu - std,
color='C0',
alpha=0.4,
lw=0)
return soln.x, mu, std
def test_grad_log_likelihood(kernel, seed=42, eps=1.34e-7):
np.random.seed(seed)
x = np.sort(np.random.rand(100))
yerr = np.random.uniform(0.1, 0.5, len(x))
y = np.sin(x)
if not terms.HAS_AUTOGRAD:
gp = GP(kernel)
gp.compute(x, yerr)
with pytest.raises(ImportError):
_, grad = gp.grad_log_likelihood(y)
return
for fit_mean in [True, False]:
gp = GP(kernel, fit_mean=fit_mean)
gp.compute(x, yerr)
_, grad = gp.grad_log_likelihood(y)
grad0 = np.empty_like(grad)
v = gp.get_parameter_vector()
for i, pval in enumerate(v):
v[i] = pval + eps
gp.set_parameter_vector(v)
ll = gp.log_likelihood(y)
v[i] = pval - eps
gp.set_parameter_vector(v)
ll -= gp.log_likelihood(y)
grad0[i] = 0.5 * ll / eps
v[i] = pval
assert np.allclose(grad, grad0)
def Fit0(x, y, yerr, verbose = True, doPlot = False, \
xpred = None, HP_init = None):
if HP_init is None:
HP_init = np.zeros(2)
k = terms.Matern32Term(log_sigma=HP_init[0], log_rho=HP_init[1])
gp = GP(k, mean=1.0)
gp.compute(x, yerr=yerr)
soln = minimize(NLL0, HP_init, jac=True, args=(gp, y))
gp.set_parameter_vector(soln.x)
if verbose:
print 'Initial pars:', HP_init
print 'Fitted pars:', soln.x
if xpred is None:
return soln.x
mu, var = gp.predict(y, xpred, return_var=True)
std = np.sqrt(var)
if doPlot:
plt.errorbar(x, y, yerr=yerr, fmt=".k", capsize=0)
plt.plot(xpred, mu, 'C0')
plt.fill_between(xpred,
mu + std,
mu - std,
color='C0',
alpha=0.4,
lw=0)
return soln.x, mu, std
def test_log_likelihood(method, seed=42):
np.random.seed(seed)
x = np.sort(np.random.rand(10))
yerr = np.random.uniform(0.1, 0.5, len(x))
y = np.sin(x)
kernel = terms.RealTerm(0.1, 0.5)
gp = GP(kernel, method=method)
with pytest.raises(RuntimeError):
gp.log_likelihood(y)
for term in [(0.6, 0.7, 1.0)]:
kernel += terms.ComplexTerm(*term)
gp = GP(kernel, method=method)
assert gp.computed is False
with pytest.raises(ValueError):
gp.compute(np.random.rand(len(x)), yerr)
gp.compute(x, yerr)
assert gp.computed is True
assert gp.dirty is False
ll = gp.log_likelihood(y)
K = gp.get_matrix(include_diagonal=True)
ll0 = -0.5 * np.dot(y, np.linalg.solve(K, y))
ll0 -= 0.5 * np.linalg.slogdet(K)[1]
ll0 -= 0.5 * len(x) * np.log(2*np.pi)
assert np.allclose(ll, ll0)
# Check that changing the parameters "un-computes" the likelihood.
gp.set_parameter_vector(gp.get_parameter_vector())
assert gp.dirty is True
assert gp.computed is False
# Check that changing the parameters changes the likelihood.
gp.compute(x, yerr)
ll1 = gp.log_likelihood(y)
params = gp.get_parameter_vector()
params[0] += 0.1
gp.set_parameter_vector(params)
gp.compute(x, yerr)
ll2 = gp.log_likelihood(y)
assert not np.allclose(ll1, ll2)
gp[1] += 0.1
assert gp.dirty is True
gp.compute(x, yerr)
ll3 = gp.log_likelihood(y)
assert not np.allclose(ll2, ll3)
class GPModel(object):
def __init__(
self,
x,
y,
n_bg_coef,
wave_err=0.05, # MAGIC NUMBER: wavelength error hack
log_sigma0=0.,
log_rho0=np.log(10.), # initial params for GP
x_shift=None):
self.x = np.array(x)
self.y = np.array(y)
if n_bg_coef >= 2:
a_kw = dict([('a{}'.format(i), 0.) for i in range(2, n_bg_coef)])
# estimate background
a_kw['a1'] = (y[-1] - y[0]) / (x[-1] - x[0]) # slope
a_kw['a0'] = y[-1] - a_kw['a1'] * x[-1] # estimate constant term
else:
a_kw = dict(a0=np.mean([y[0], y[-1]]))
# initialize model
self.mean_model = MeanModel(n_bg_coef=n_bg_coef, **a_kw)
self.kernel = terms.Matern32Term(log_sigma=log_sigma0,
log_rho=log_rho0)
# set up the gp
self.gp = GP(self.kernel, mean=self.mean_model, fit_mean=True)
self.gp.compute(x, yerr=wave_err)
logger.log(
0, "Initial log-likelihood: {0}".format(self.gp.log_likelihood(y)))
if x_shift is None:
self.x_shift = 0.
else:
self.x_shift = x_shift
def neg_ln_like(self, params):
# minimize -log(likelihood)
self.gp.set_parameter_vector(params)
ll = self.gp.log_likelihood(self.y)
if np.isnan(ll):
return np.inf
return -ll
def __call__(self, params):
return self.neg_ln_like(params)
def learn_gps(self):
for lcid in tqdm(self.lcids, desc='Learning GPs', leave=False):
kernel = Matern32Term(log(self.lpf.fluxes[lcid].std()), log(0.1))
gp = GP(kernel, mean=0.0)
gp.freeze_parameter('kernel:log_sigma')
def nll(x):
gp.set_parameter_vector(x)
gp.compute(self.lpf.times[lcid], self.lpf.wn[lcid])
return -gp.log_likelihood(self.lpf.fluxes[lcid] - 1.0)
res = minimize(nll, [log(1.)])
gp.set_parameter_vector(res.x)
gp.compute(self.lpf.times[lcid], self.lpf.wn[lcid])
self.gps.append(gp)
def test_grad_log_likelihood(kernel, with_general, seed=42, eps=1.34e-7):
np.random.seed(seed)
x = np.sort(np.random.rand(100))
yerr = np.random.uniform(0.1, 0.5, len(x))
y = np.sin(x)
if with_general:
U = np.vander(x - np.mean(x), 4).T
V = U * np.random.rand(4)[:, None]
A = np.sum(U * V, axis=0) + 1e-8
else:
A = np.empty(0)
U = np.empty((0, 0))
V = np.empty((0, 0))
if not terms.HAS_AUTOGRAD:
gp = GP(kernel)
gp.compute(x, yerr, A=A, U=U, V=V)
with pytest.raises(ImportError):
_, grad = gp.grad_log_likelihood(y)
return
for fit_mean in [True, False]:
gp = GP(kernel, fit_mean=fit_mean)
gp.compute(x, yerr, A=A, U=U, V=V)
_, grad = gp.grad_log_likelihood(y)
grad0 = np.empty_like(grad)
v = gp.get_parameter_vector()
for i, pval in enumerate(v):
v[i] = pval + eps
gp.set_parameter_vector(v)
ll = gp.log_likelihood(y)
v[i] = pval - eps
gp.set_parameter_vector(v)
ll -= gp.log_likelihood(y)
grad0[i] = 0.5 * ll / eps
v[i] = pval
assert np.allclose(grad, grad0)
def test_build_gp(method, seed=42):
kernel = terms.RealTerm(0.5, 0.1)
kernel += terms.ComplexTerm(0.6, 0.7, 1.0)
gp = GP(kernel, method=method)
assert gp.vector_size == 5
p = gp.get_parameter_vector()
assert np.allclose(p, [0.5, 0.1, 0.6, 0.7, 1.0])
gp.set_parameter_vector([0.5, 0.8, 0.6, 0.7, 2.0])
p = gp.get_parameter_vector()
assert np.allclose(p, [0.5, 0.8, 0.6, 0.7, 2.0])
with pytest.raises(ValueError):
gp.set_parameter_vector([0.5, 0.8, -0.6])
with pytest.raises(ValueError):
gp.set_parameter_vector("face1")
class LineFitter(object):
def __init__(self,
x,
flux,
ivar=None,
absorp_emiss=None,
n_bg_coef=2,
target_x=None):
"""
Parameters
----------
x : array_like
Dispersion parameter. Usually either pixel or wavelength.
flux : array_like
Flux array.
ivar : array_like
Inverse-variance array.
absorp_emiss : numeric [-1, 1] (optional)
If -1, absorption line. If +1, emission line. If not specified,
will try to guess.
n_bg_coef : int (optional)
The order of the polynomial used to fit the background.
1 = constant, 2 = linear, 3 = quadratic, etc.
target_x : numeric (optional)
Where we think the line of interest is.
"""
self.x = np.array(x)
self.flux = np.array(flux)
if ivar is not None:
self.ivar = np.array(ivar)
self._err = 1 / np.sqrt(self.ivar)
else:
self.ivar = np.ones_like(flux)
self._err = None
if absorp_emiss is None:
raise NotImplementedError(
"You must supply an absorp_emiss for now")
self.absorp_emiss = float(absorp_emiss)
self.target_x = target_x
self.n_bg_coef = int(n_bg_coef)
# result of fitting
self.gp = None
self.success = None
@classmethod
def transform_pars(cls, p):
new_p = OrderedDict()
for k, v in p.items():
if k in cls._log_pars:
k = 'ln_{0}'.format(k)
v = np.log(v)
new_p[k] = v
return new_p
def get_init_generic(self, amp=None, x0=None, bg=None, bg_buffer=None):
"""
Get initial guesses for the generic line parameters.
Parameters
----------
amp : numeric
Line amplitude. This should be strictly positive; the
``absorp_emiss`` parameter controls whether it is absorption or
emission.
x0 : numeric
Line centroid.
bg : iterable
Background polynomial coefficients.
bg_buffer : int
The number of values to use on either end of the flux array to
estimate the background parameters.
"""
target_x = self.target_x
if x0 is None: # estimate the initial guess for the centroid
relmins = argrelmin(-self.absorp_emiss * self.flux)[0]
if len(relmins) > 1 and target_x is None:
logger.log(
0, "no target_x specified - taking largest line "
"in spec region")
target_x = self.x[np.argmin(-self.absorp_emiss * self.flux)]
if len(relmins) == 1:
x0 = self.x[relmins[0]]
else:
x0_idx = relmins[np.abs(self.x[relmins] - target_x).argmin()]
x0 = self.x[x0_idx]
# shift x array so that line is approximately at 0
_x = np.array(self.x, copy=True)
x = np.array(_x) - x0
# background polynomial parameters
if bg_buffer is None:
bg_buffer = len(x) // 4
bg_buffer = max(1, bg_buffer)
if bg is None:
if self.n_bg_coef < 2:
bg = np.array([0.])
bg[0] = np.median(self.flux)
else:
# estimate linear background model
bg = np.array([0.] * self.n_bg_coef)
i1 = argmedian(self.flux[:bg_buffer])
i2 = argmedian(self.flux[-bg_buffer:])
f1 = self.flux[:bg_buffer][i1]
f2 = self.flux[-bg_buffer:][i2]
x1 = x[:bg_buffer][i1]
x2 = x[-bg_buffer:][i2]
bg[1] = (f2 - f1) / (x2 - x1) # slope
bg[0] = f2 - bg[1] * x2 # estimate constant term
else:
if len(bg) != self.n_bg_coef:
raise ValueError('Number of bg polynomial coefficients does '
'not match n_bg_coef specified when fitter '
'was created.')
if amp is None: # then estimate the initial guess for amplitude
_i = np.argmin(np.abs(x))
if len(bg) > 1:
_bg = bg[0] + bg[1] * x[_i]
else:
_bg = bg[0]
# amp = np.sqrt(2*np.pi) * (flux[_i] - bg)
amp = self.flux[_i] - _bg
p0 = OrderedDict()
p0['amp'] = np.abs(amp)
p0['x0'] = x0
p0['bg_coef'] = bg
return p0
def get_init_gp(self, log_sigma=None, log_rho=None, x0=None):
"""
Set up the GP kernel parameters.
"""
if log_sigma is None:
if x0 is not None:
# better initial guess for GP parameters
mask = np.abs(self.x - x0) > 2.
y_MAD = np.median(
np.abs(self.flux[mask] - np.median(self.flux[mask])))
else:
y_MAD = np.median(np.abs(self.flux - np.median(self.flux)))
log_sigma = np.log(3 * y_MAD)
if log_rho is None:
log_rho = np.log(5.)
p0 = OrderedDict()
p0['log_sigma'] = log_sigma
p0['log_rho'] = log_rho
return p0
def init_gp(self,
log_sigma=None,
log_rho=None,
amp=None,
x0=None,
bg=None,
bg_buffer=None,
**kwargs):
"""
**kwargs:
"""
# Call the different get_init methods with the correct kwargs passed
sig = inspect.signature(self.get_init)
kw = OrderedDict()
for k in list(sig.parameters.keys()):
kw[k] = kwargs.pop(k, None)
p0 = self.get_init(**kw)
# Call the generic init method - all line models must have these params
p0_generic = self.get_init_generic(amp=amp,
x0=x0,
bg=bg,
bg_buffer=bg_buffer)
for k, v in p0_generic.items():
p0[k] = v
# expand bg parameters
bgs = p0.pop('bg_coef')
for i in range(self.n_bg_coef):
p0['bg{}'.format(i)] = bgs[i]
# transform
p0 = self.transform_pars(p0)
# initialize model
mean_model = self.MeanModel(n_bg_coef=self.n_bg_coef,
absorp_emiss=self.absorp_emiss,
**p0)
p0_gp = self.get_init_gp(log_sigma=log_sigma, log_rho=log_rho)
kernel = terms.Matern32Term(log_sigma=p0_gp['log_sigma'],
log_rho=p0_gp['log_rho'])
# set up the gp model
self.gp = GP(kernel, mean=mean_model, fit_mean=True)
if self._err is not None:
self.gp.compute(self.x, self._err)
else:
self.gp.compute(self.x)
init_params = self.gp.get_parameter_vector()
init_ll = self.gp.log_likelihood(self.flux)
logger.log(0, "Initial log-likelihood: {0}".format(init_ll))
return init_params
def get_gp_mean_pars(self):
"""
Return a parameter dictionary for the mean model parameters only.
"""
fit_pars = OrderedDict()
for k, v in self.gp.get_parameter_dict().items():
if 'mean' not in k:
continue
k = k[5:] # remove 'mean:'
if k.startswith('ln'):
if 'amp' in k:
fit_pars[k[3:]] = self.absorp_emiss * np.exp(v)
else:
fit_pars[k[3:]] = np.exp(v)
elif k.startswith('bg'):
if 'bg_coef' not in fit_pars:
fit_pars['bg_coef'] = []
fit_pars['bg_coef'].append(v)
else:
fit_pars[k] = v
return fit_pars
def _neg_log_like(self, params):
self.gp.set_parameter_vector(params)
try:
ll = self.gp.log_likelihood(self.flux)
except (RuntimeError, LinAlgError):
return np.inf
if np.isnan(ll):
return np.inf
return -ll
def fit(self, bounds=None, **kwargs):
"""
"""
init_params = self.init_gp()
if bounds is None:
bounds = OrderedDict()
# default bounds for mean model parameters
i = self.gp.models['mean'].get_parameter_names().index('x0')
mean_bounds = self.gp.models['mean'].get_parameter_bounds()
if mean_bounds[i][0] is None and mean_bounds[i][1] is None:
mean_bounds[i] = (min(self.x), max(self.x))
for i, k in enumerate(self.gp.models['mean'].parameter_names):
mean_bounds[i] = bounds.get(k, mean_bounds[i])
self.gp.models['mean'].parameter_bounds = mean_bounds
# HACK: default bounds for kernel parameters
self.gp.models['kernel'].parameter_bounds = [(None, None),
(np.log(0.5), None)]
soln = minimize(self._neg_log_like,
init_params,
method="L-BFGS-B",
bounds=self.gp.get_parameter_bounds())
self.success = soln.success
self.gp.set_parameter_vector(soln.x)
if self.success:
logger.debug("Success: {0}, Final log-likelihood: {1}".format(
soln.success, -soln.fun))
else:
logger.warning("Fit failed! Final log-likelihood: {0}, "
"Final parameters: {1}".format(-soln.fun, soln.x))
return self
def plot_fit(self, axes=None, fit_alpha=0.5):
unbinned_color = '#3182bd'
binned_color = '#2ca25f'
gp_color = '#ff7f0e'
noise_color = '#de2d26'
if self.gp is None:
raise ValueError("You must run .fit() first!")
# ----------------------------------------------------------------------
# Plot the maximum likelihood model
if axes is None:
fig, axes = plt.subplots(1, 3, figsize=(15, 5), sharex=True)
# data
for ax in axes[:2]:
ax.plot(self.x,
self.flux,
drawstyle='steps-mid',
marker='',
color='#777777',
zorder=2)
if self._err is not None:
ax.errorbar(self.x,
self.flux,
self._err,
marker='',
ls='none',
ecolor='#666666',
zorder=1)
# mean model
wave_grid = np.linspace(self.x.min(), self.x.max(), 256)
mu, var = self.gp.predict(self.flux, self.x, return_var=True)
std = np.sqrt(var)
axes[0].plot(wave_grid,
self.gp.mean.get_unbinned_value(wave_grid),
marker='',
alpha=fit_alpha,
zorder=10,
color=unbinned_color)
axes[0].plot(self.x,
self.gp.mean.get_value(self.x),
marker='',
alpha=fit_alpha,
zorder=10,
drawstyle='steps-mid',
color=binned_color)
# full GP model
axes[1].plot(self.x,
mu,
color=gp_color,
drawstyle='steps-mid',
marker='',
alpha=fit_alpha,
zorder=10)
axes[1].fill_between(self.x,
mu + std,
mu - std,
color=gp_color,
alpha=fit_alpha / 10.,
edgecolor="none",
step='mid')
# just GP noise component
mean_model = self.gp.mean.get_value(self.x)
axes[2].plot(self.x,
mu - mean_model,
marker='',
alpha=fit_alpha,
zorder=10,
drawstyle='steps-mid',
color=noise_color)
axes[2].plot(self.x,
self.flux - mean_model,
drawstyle='steps-mid',
marker='',
color='#777777',
zorder=2)
if self._err is not None:
axes[2].errorbar(self.x,
self.flux - mean_model,
self._err,
marker='',
ls='none',
ecolor='#666666',
zorder=1)
axes[0].set_ylabel('flux')
axes[0].set_xlim(self.x.min(), self.x.max())
axes[0].set_title('Line model')
axes[1].set_title('Line + noise model')
axes[2].set_title('Noise model')
fig = axes[0].figure
fig.tight_layout()
return fig
class CeleriteLogLikelihood:
def __init__(self, lpf, name: str = 'gp', noise_ids=None, fixed_hps=None):
if not with_celerite:
raise ImportError("CeleriteLogLikelihood requires celerite.")
self.name = name
self.lpf = lpf
if fixed_hps is None:
self.free = True
else:
self.hps = asarray(fixed_hps)
self.free = False
if lpf.lcids is None:
raise ValueError(
'The LPF data needs to be initialised before initialising CeleriteLogLikelihood.'
)
self.noise_ids = noise_ids if noise_ids is not None else unique(
lpf.noise_ids)
self.mask = m = zeros(lpf.lcids.size, bool)
for lcid, nid in enumerate(lpf.noise_ids):
if nid in self.noise_ids:
m[lcid == lpf.lcids] = 1
if m.sum() == lpf.lcids.size:
self.times = lpf.timea
self.fluxes = lpf.ofluxa
else:
self.times = lpf.timea[m]
self.fluxes = lpf.ofluxa[m]
self.gp = GP(Matern32Term(0, 0))
if self.free:
self.init_parameters()
else:
self.compute_gp(None, force=True, hps=self.hps)
def init_parameters(self):
name = self.name
wns = log10(mad_std(diff(self.fluxes)) / sqrt(2))
pgp = [
LParameter(f'{name}_ln_out',
f'{name} ln output scale',
'',
NP(-6, 1.5),
bounds=(-inf, inf)),
LParameter(f'{name}_ln_in',
f'{name} ln input scale',
'',
UP(-8, 8),
bounds=(-inf, inf)),
LParameter(f'{name}_log10_wn',
f'{name} log10 white noise sigma',
'',
NP(wns, 0.025),
bounds=(-inf, inf))
]
self.lpf.ps.thaw()
self.lpf.ps.add_global_block(self.name, pgp)
self.lpf.ps.freeze()
self.pv_slice = self.lpf.ps.blocks[-1].slice
self.pv_start = self.lpf.ps.blocks[-1].start
setattr(self.lpf, f"_sl_{name}", self.pv_slice)
setattr(self.lpf, f"_start_{name}", self.pv_start)
def compute_gp(self, pv, force: bool = False, hps=None):
if self.free or force:
parameters = pv[self.pv_slice] if hps is None else hps
self.gp.set_parameter_vector(parameters[:-1])
self.gp.compute(self.times, yerr=10**parameters[-1])
def compute_gp_lnlikelihood(self, pv, model):
self.compute_gp(pv)
return self.gp.log_likelihood(self.fluxes - model[self.mask])
def predict_baseline(self, pv):
self.compute_gp(pv)
residuals = self.fluxes - squeeze(
self.lpf.transit_model(pv))[self.mask]
bl = zeros_like(self.lpf.timea)
bl[self.mask] = self.gp.predict(residuals,
self.times,
return_cov=False)
return 1. + bl
def __call__(self, pvp, model):
if pvp.ndim == 1:
lnlike = self.compute_gp_lnlikelihood(pvp, model)
else:
lnlike = zeros(pvp.shape[0])
for ipv, pv in enumerate(pvp):
if all(isfinite(model[ipv])):
lnlike[ipv] = self.compute_gp_lnlikelihood(pv, model[ipv])
else:
lnlike[ipv] = -inf
return lnlike
def main(output_path):
## test DRW
drw_kernel = DRW_term(np.log(0.3), np.log(250))
ndpts = [100, 1_000, 10_000, 100_000]
max_dpt = ndpts[-1]
drw_dts = []
gp_fit_drw = GP(drw_kernel)
init_params = drw_kernel.get_parameter_vector()
for dpts in ndpts:
# must reset to avoid unstable parameters
gp_fit_drw.set_parameter_vector(init_params)
t, y, yerr = gpSimRand(drw_kernel,
100,
10 * 3650,
dpts,
full_N=max_dpt * 3)
drw_std = np.sqrt(np.var(y) - np.var(yerr))
gp_fit_drw.compute(t[0], yerr[0])
start = time.time()
for i in range(100):
neg_ll(init_params, y[0], yerr[0], gp_fit_drw)
drw_dts.append(time.time() - start)
## test DHO
dho_kernel = DHO_term(*dho_log_param_init())
dho_dts = []
gp_fit_dho = GP(dho_kernel)
init_params = dho_kernel.get_parameter_vector()
for dpts in ndpts:
gp_fit_dho.set_parameter_vector(
init_params) # must reset to avoid unstable parameters
t, y, yerr = gpSimRand(dho_kernel,
100,
10 * 3650,
dpts,
full_N=max_dpt * 3)
gp_fit_dho.compute(t[0], yerr[0])
start = time.time()
for i in range(100):
neg_ll(init_params, y[0], yerr[0], gp_fit_dho)
dho_dts.append(time.time() - start)
## CARMA(3,0)
p = 3
q = 0
carma30a = CARMA_term(np.log([3, 3.25, 1.2]), np.log([1]))
params = carma30a.get_parameter_vector()
carma_30_dts = []
gp_fit_carma_30 = GP(carma30a)
for dpts in ndpts:
gp_fit_carma_30.set_parameter_vector(
params) # must reset to avoid unstable parameters
t, y, yerr = gpSimRand(carma30a,
100,
10 * 3650,
dpts,
full_N=max_dpt * 3)
gp_fit_carma_30.compute(t[0], y[0])
start = time.time()
for i in range(100):
neg_ll(params, y[0], yerr[0], gp_fit_carma_30)
carma_30_dts.append(time.time() - start)
# save to file
df = pd.DataFrame({
"data points": ndpts,
"drw": np.array(drw_dts) / 100,
"dho": np.array(dho_dts) / 100,
"carma_30": np.array(carma_30_dts) / 100,
})
df.to_csv(output_path, index=False)
def drw_fit(lc_df, de=True, debug=False, plot=False, bounds=None):
best_fit = np.zeros((2, 6))
# fail_num = 0
lc_df = lc_df.copy()
std = np.std(lc_df.flux.values)
if bounds is not None:
first_bounds = bounds
else:
first_bounds = [(-4, np.log(4 * std)), (-4, 10)]
# loop through lc in each passband
for band in range(6):
try:
lc_band = lc_df[lc_df.passband == band].copy()
t = lc_band.mjd.values - lc_band.mjd.min()
y = lc_band.flux.values
yerr = lc_band.flux_err.values
rerun = True # dynamic control of bounds
counter = 0
bounds = first_bounds
jac_log_rec = 10
# initialize parameter and kernel
kernel = DRW_term(*drw_log_param_init(std))
gp = GP(kernel, mean=np.mean(y))
gp.compute(t, yerr)
if de:
# set bound based on LC std for amp
while rerun and (counter < 5):
counter += 1
r = differential_evolution(neg_ll,
bounds=bounds,
args=(y, yerr, gp),
maxiter=200)
if r.success:
best_fit[:, band] = np.exp(r.x)
if "jac" not in r.keys():
rerun = False
else:
jac_log = np.log10(np.dot(r.jac, r.jac) + 1e-8)
# if positive jac, then increase bounds
if jac_log > 0:
bounds = [(x[0] - 1, x[1] + 1) for x in bounds]
else:
rerun = False
# update best-fit if smaller jac found
if jac_log < jac_log_rec:
jac_log_rec = jac_log
best_fit[:, band] = np.exp(r.x)
else:
bounds = [(x[0] - 1, x[1] + 1) for x in bounds]
gp.set_parameter_vector(drw_log_param_init(std))
else:
initial_params = gp.get_parameter_vector()
while rerun and (counter < 5):
counter += 1
r = minimize(
neg_ll,
initial_params,
method="L-BFGS-B",
bounds=bounds,
args=(y, yerr, gp),
)
if r.success:
best_fit[:, band] = np.exp(r.x)
if "jac" not in r.keys():
rerun = False
else:
jac_log = np.log10(np.dot(r.jac, r.jac) + 1e-8)
# if positive jac, then increase bounds
if jac_log > 0:
bounds = [(x[0] - 1, x[1] + 1) for x in bounds]
else:
rerun = False
# update best-fit if smaller jac found
if jac_log < jac_log_rec:
jac_log_rec = jac_log
best_fit[:, band] = np.exp(r.x)
else:
bounds = [(x[0] - 1, x[1] + 1) for x in bounds]
gp.set_parameter_vector(drw_log_param_init(std))
if not r.success:
best_fit[:, band] = np.nan
except Exception as e:
print(r)
print(e)
print(
f"Exception at object_id: {lc_df.object_id.values[0]}, passband: {band}"
)
best_fit[:, band] = np.nan
# fail_num += 1
# Below code is used to visualize if stuck in local minima
if debug:
print(r)
if plot:
plot_drw_ll(t, y, yerr, np.exp(r.x), gp, vec_neg_ll)
return np.concatenate([[lc_df.object_id.values[0]], best_fit.flatten()])
def carma_fit(lc_df, p, q, de=True, debug=False, plot=False, bounds=None):
best_fit = np.zeros((int(p + q + 1), 6))
lc_df = lc_df.copy()
if bounds is not None:
first_bounds = bounds
else:
first_bounds = [(-10, 5)] * int(p + q + 1)
# loop through lc in each passband
for band in range(6):
try:
lc_band = lc_df[lc_df.passband == band].copy()
t = lc_band.mjd.values - lc_band.mjd.min()
y = lc_band.flux.values
yerr = lc_band.flux_err.values
rerun = True # dynamic control of bounds
compute = True # handle can't factorize in gp.compute()
succeded = False # ever succeded
compute_ct = 0
counter = 0
bounds = first_bounds
jac_log_rec = 10
# initialize parameter, kernel and GP
log_params = carma_param_init(int(p + q + 1))
kernel = CARMA_term(log_params[:p], log_params[p:])
gp = GP(kernel, mean=np.mean(y))
# compute can't factorize, try 4 more times
while compute & (compute_ct < 5):
compute_ct += 1
try:
gp.compute(t, yerr)
compute = False
except celerite.solver.LinAlgError:
gp.set_parameter_vector(carma_param_init(int(p + q + 1)))
if de:
# set bound based on LC std for amp
while rerun and (counter < 5):
counter += 1
r = differential_evolution(neg_ll,
bounds=bounds,
args=(y, yerr, gp),
maxiter=200)
if r.success:
succeded = True
best_fit[:, band] = np.exp(r.x)
if "jac" not in r.keys():
rerun = False
else:
jac_log = np.log10(np.dot(r.jac, r.jac) + 1e-8)
# if positive jac, then increase bounds
if jac_log > 0:
bounds = [(x[0] - 1, x[1] + 1) for x in bounds]
else:
rerun = False
# update best-fit if smaller jac found
if jac_log < jac_log_rec:
jac_log_rec = jac_log
best_fit[:, band] = np.exp(r.x)
else:
bounds = [(x[0] - 1, x[1] + 1) for x in bounds]
gp.set_parameter_vector(
carma_param_init(int(p + q + 1)))
else:
initial_params = gp.get_parameter_vector()
while rerun and (counter < 5):
counter += 1
r = minimize(
neg_ll,
initial_params,
method="L-BFGS-B",
bounds=bounds,
args=(y, yerr, gp),
)
if r.success:
succeded = True
best_fit[:, band] = np.exp(r.x)
jac_log = np.log10(np.dot(r.jac, r.jac) + 1e-8)
# if positive jac, then increase bounds
if jac_log > 0:
bounds = [(x[0] - 1, x[1] + 1) for x in bounds]
else:
rerun = False
# update best-fit if smaller jac found
if jac_log < jac_log_rec:
jac_log_rec = jac_log
best_fit[:, band] = np.exp(r.x)
else:
bounds = [(x[0] - 1, x[1] + 1) for x in bounds]
gp.set_parameter_vector(
carma_param_init(int(p + q + 1)))
if not succeded:
best_fit[:, band] = np.nan
except Exception as e:
print(e)
print(
f"Exception at object_id: {lc_df.object_id.values[0]}, passband: {band}"
)
best_fit[:, band] = np.nan
# Below code is used to visualize if stuck in local minima
if debug:
print(r)
# if plot:
# plot_dho_ll(t, y, yerr, np.exp(r.x), gp, vec_neg_ll)
return np.concatenate([[lc_df.object_id.values[0]], best_fit.flatten()])
def test_log_likelihood(seed=42):
np.random.seed(seed)
x = np.sort(np.random.rand(10))
yerr = np.random.uniform(0.1, 0.5, len(x))
y = np.sin(x)
kernel = terms.RealTerm(0.1, 0.5)
gp = GP(kernel)
with pytest.raises(RuntimeError):
gp.log_likelihood(y)
termlist = [(0.1 + 10./j, 0.5 + 10./j) for j in range(1, 4)]
termlist += [(1.0 + 10./j, 0.01 + 10./j, 0.5, 0.01) for j in range(1, 10)]
termlist += [(0.6, 0.7, 1.0), (0.3, 0.05, 0.5, 0.6)]
for term in termlist:
if len(term) > 2:
kernel += terms.ComplexTerm(*term)
else:
kernel += terms.RealTerm(*term)
gp = GP(kernel)
assert gp.computed is False
with pytest.raises(ValueError):
gp.compute(np.random.rand(len(x)), yerr)
gp.compute(x, yerr)
assert gp.computed is True
assert gp.dirty is False
ll = gp.log_likelihood(y)
K = gp.get_matrix(include_diagonal=True)
ll0 = -0.5 * np.dot(y, np.linalg.solve(K, y))
ll0 -= 0.5 * np.linalg.slogdet(K)[1]
ll0 -= 0.5 * len(x) * np.log(2*np.pi)
assert np.allclose(ll, ll0)
# Check that changing the parameters "un-computes" the likelihood.
gp.set_parameter_vector(gp.get_parameter_vector())
assert gp.dirty is True
assert gp.computed is False
# Check that changing the parameters changes the likelihood.
gp.compute(x, yerr)
ll1 = gp.log_likelihood(y)
params = gp.get_parameter_vector()
params[0] += 10.0
gp.set_parameter_vector(params)
gp.compute(x, yerr)
ll2 = gp.log_likelihood(y)
assert not np.allclose(ll1, ll2)
gp[1] += 10.0
assert gp.dirty is True
gp.compute(x, yerr)
ll3 = gp.log_likelihood(y)
assert not np.allclose(ll2, ll3)
# Test zero delta t
ind = len(x) // 2
x = np.concatenate((x[:ind], [x[ind]], x[ind:]))
y = np.concatenate((y[:ind], [y[ind]], y[ind:]))
yerr = np.concatenate((yerr[:ind], [yerr[ind]], yerr[ind:]))
gp.compute(x, yerr)
ll = gp.log_likelihood(y)
K = gp.get_matrix(include_diagonal=True)
ll0 = -0.5 * np.dot(y, np.linalg.solve(K, y))
ll0 -= 0.5 * np.linalg.slogdet(K)[1]
ll0 -= 0.5 * len(x) * np.log(2*np.pi)
assert np.allclose(ll, ll0), "face"
def test_log_likelihood(with_general, seed=42):
np.random.seed(seed)
x = np.sort(np.random.rand(10))
yerr = np.random.uniform(0.1, 0.5, len(x))
y = np.sin(x)
if with_general:
U = np.vander(x - np.mean(x), 4).T
V = U * np.random.rand(4)[:, None]
A = np.sum(U * V, axis=0) + 1e-8
else:
A = np.empty(0)
U = np.empty((0, 0))
V = np.empty((0, 0))
# Check quiet argument with a non-positive definite kernel.
class NPDTerm(terms.Term):
parameter_names = ("par1", )
def get_real_coefficients(self, params): # NOQA
return [params[0]], [0.1]
gp = GP(NPDTerm(-1.0))
with pytest.raises(celerite.solver.LinAlgError):
gp.compute(x, 0.0)
with pytest.raises(celerite.solver.LinAlgError):
gp.log_likelihood(y)
assert np.isinf(gp.log_likelihood(y, quiet=True))
if terms.HAS_AUTOGRAD:
assert np.isinf(gp.grad_log_likelihood(y, quiet=True)[0])
kernel = terms.RealTerm(0.1, 0.5)
gp = GP(kernel)
with pytest.raises(RuntimeError):
gp.log_likelihood(y)
termlist = [(0.1 + 10. / j, 0.5 + 10. / j) for j in range(1, 4)]
termlist += [(1.0 + 10. / j, 0.01 + 10. / j, 0.5, 0.01)
for j in range(1, 10)]
termlist += [(0.6, 0.7, 1.0), (0.3, 0.05, 0.5, 0.6)]
for term in termlist:
if len(term) > 2:
kernel += terms.ComplexTerm(*term)
else:
kernel += terms.RealTerm(*term)
gp = GP(kernel)
assert gp.computed is False
with pytest.raises(ValueError):
gp.compute(np.random.rand(len(x)), yerr)
gp.compute(x, yerr, A=A, U=U, V=V)
assert gp.computed is True
assert gp.dirty is False
ll = gp.log_likelihood(y)
K = gp.get_matrix(include_diagonal=True)
ll0 = -0.5 * np.dot(y, np.linalg.solve(K, y))
ll0 -= 0.5 * np.linalg.slogdet(K)[1]
ll0 -= 0.5 * len(x) * np.log(2 * np.pi)
assert np.allclose(ll, ll0)
# Check that changing the parameters "un-computes" the likelihood.
gp.set_parameter_vector(gp.get_parameter_vector())
assert gp.dirty is True
assert gp.computed is False
# Check that changing the parameters changes the likelihood.
gp.compute(x, yerr, A=A, U=U, V=V)
ll1 = gp.log_likelihood(y)
params = gp.get_parameter_vector()
params[0] += 10.0
gp.set_parameter_vector(params)
gp.compute(x, yerr, A=A, U=U, V=V)
ll2 = gp.log_likelihood(y)
assert not np.allclose(ll1, ll2)
gp[1] += 10.0
assert gp.dirty is True
gp.compute(x, yerr, A=A, U=U, V=V)
ll3 = gp.log_likelihood(y)
assert not np.allclose(ll2, ll3)
# Test zero delta t
ind = len(x) // 2
x = np.concatenate((x[:ind], [x[ind]], x[ind:]))
y = np.concatenate((y[:ind], [y[ind]], y[ind:]))
yerr = np.concatenate((yerr[:ind], [yerr[ind]], yerr[ind:]))
gp.compute(x, yerr)
ll = gp.log_likelihood(y)
K = gp.get_matrix(include_diagonal=True)
ll0 = -0.5 * np.dot(y, np.linalg.solve(K, y))
ll0 -= 0.5 * np.linalg.slogdet(K)[1]
ll0 -= 0.5 * len(x) * np.log(2 * np.pi)
assert np.allclose(ll, ll0)
def GPSpec_1Comp(wav, flux, flux_err, nsteps=2000, nrange=3, prefix='RR1'):
# NB: input wavelengths should be in nm, flux continuum should be about 1
K, N = wav.shape
# Create 2-D array of scaled log wavelengths for fitting
lwav = np.log(wav * 1e-9) # in m
lw0, lw1 = lwav.min(), lwav.max()
x = (lwav - lw0) / (lw1 - lw0)
# First do GP fit to individual spectra to get estimate of GP HPs
print 'GP fit to individual spectra'
HPs = np.zeros((K, 2))
for i in range(K):
xx = x[i, :].flatten()
yy = flux[i, :].flatten()
ee = flux_err[i, :].flatten()
HPs[i, :] = Fit0(xx, yy, ee, verbose=False, xpred=None)
HPs = np.median(HPs, axis=0)
print 'Initial GP HPs:', HPs
# Initial (ML) estimate of parameters
print "Starting ML fit"
par_in = np.zeros(K + 1)
par_in[-2:] = HPs
ML_par = np.array(Fit1(x, flux, flux_err, verbose=False, par_in=par_in))
par_ML = np.copy(ML_par)
par_ML[:K - 1] *= (lw1 - lw0) * SPEED_OF_LIGHT * 1e-3
par_ML[-1] *= (lw1 - lw0)
k = terms.Matern32Term(log_sigma=ML_par[-2], log_rho=ML_par[-1])
gp = GP(k, mean=1.0)
print "ML fit done"
# MCMC
print "Starting MCMC"
ndim = K + 1
nwalkers = ndim * 4
p0 = ML_par + 1e-4 * np.random.randn(nwalkers, ndim)
sampler = emcee.EnsembleSampler(nwalkers,
ndim,
LP1,
args=[gp, x, flux, flux_err])
for i, result in enumerate(sampler.sample(p0, iterations=nsteps)):
n = int((30 + 1) * float(i) / nsteps)
sys.stdout.write("\r[{0}{1}]".format('#' * n, ' ' * (30 - n)))
sys.stdout.write("\n")
print("MCMC done")
# find MAP parameters
iMAP = np.argmax(sampler.flatlnprobability)
MAP_par = sampler.flatchain[iMAP, :].flatten()
# extract MCMC chains
samples = sampler.chain
Lprob = sampler.lnprobability
# convert chains back to physical units: shifts in km/s
samples_tpl = np.copy(samples)
samples_tpl[:, :, :K - 1] *= (lw1 - lw0) * SPEED_OF_LIGHT * 1e-3
samples_tpl[:, :, -1] *= (lw1 - lw0)
par_MAP = np.copy(MAP_par)
par_MAP[:K - 1] *= (lw1 - lw0) * SPEED_OF_LIGHT * 1e-3
par_MAP[-1] *= (lw1 - lw0)
# parameter names for plots
labels = []
for i in range(K - 1):
labels.append(r'$\delta v_{%d}$ (km/s)' % (i + 1))
labels.append(r'$\ln \sigma$')
labels.append(r'$\ln \rho$')
labels = np.array(labels)
names = []
for i in range(K - 1):
names.append('dv_%d (km/s)' % (i + 1))
names.append('ln(sig)')
names.append('ln(rho)')
names = np.array(names)
# Plot the chains
fig1 = plt.figure(figsize=(12, K + 3))
gs1 = gridspec.GridSpec(ndim + 1, 1)
gs1.update(left=0.1, right=0.98, bottom=0.07, top=0.98, hspace=0)
ax1 = plt.subplot(gs1[0, 0])
plt.setp(ax1.get_xticklabels(), visible=False)
plt.plot(Lprob.T, 'k-', alpha=0.2)
plt.ylabel(r'$\ln P$')
for i in range(ndim):
axc = plt.subplot(gs1[i + 1, 0], sharex=ax1)
if i < (ndim - 1):
plt.setp(axc.get_xticklabels(), visible=False)
plt.plot(samples_tpl[:, :, i].T, 'k-', alpha=0.2)
plt.ylabel(labels[i])
plt.xlim(0, nsteps)
plt.xlabel('iteration number')
# Discard burnout
nburn = int(raw_input('Enter no. steps to discard as burnout: '))
plt.axvline(nburn)
# Evaluate and print the parameter ranges
print '\n{:20s}: {:10s} {:10s} {:10s} - {:7s} + {:7s}'.format('Parameter', 'ML', 'MAP', \
'Median','Error','Error')
par50 = np.zeros(ndim)
par84 = np.zeros(ndim)
par16 = np.zeros(ndim)
for i in range(ndim):
sam = samples_tpl[:, nburn:, i].flatten()
b, m, f = np.percentile(sam, [16, 50, 84])
par50[i] = m
par16[i] = b
par84[i] = f
print '{:20s}: {:10.5f} {:10.5f} {:10.5f} - {:7.5f} + {:7.5f}'.format(names[i], \
par_ML[i], \
par_MAP[i], \
m, m-b, f-m)
if prefix is None:
return par_MAP, par50, par50 - par16, par84 - par50
plt.savefig('%s_chains.png' % prefix)
samples_flat = samples[:, nburn:, :].reshape(-1, ndim)
samples_tpl_flat = samples_tpl[:, nburn:, :].reshape(-1, ndim)
# Plot the parameter distributions
fig2 = corner.corner(samples_tpl_flat, truths = par_MAP, labels = labels, show_titles = True, \
quantiles = [0.16, 0.84])
plt.savefig('%s_corner.png' % prefix)
# Plot the individual spectra with MAP fit
xpred, fpred, fpred_err = Pred1_2D(MAP_par,
x,
flux,
flux_err,
doPlot=False)
lwpred = (lw1 - lw0) * xpred + lw0
wpred = np.exp(lwpred) * 1e9
fig3 = plt.figure(figsize=(12, K + 1))
gs3 = gridspec.GridSpec(K, 1)
gs3.update(left=0.1, right=0.98, bottom=0.07, top=0.98, hspace=0)
for i in range(K):
if i == 0:
ax1 = plt.subplot(gs3[0, 0])
else:
axc = plt.subplot(gs3[i, 0], sharex=ax1, sharey=ax1)
if i < (K - 1):
plt.setp(ax1.get_xticklabels(), visible=False)
plt.errorbar(wav[i,:], flux[i,:], yerr = flux_err[i,:], \
fmt = ".k", ms = 2, mec = 'none', capsize = 0, alpha = 0.5)
plt.plot(wpred[i, :], fpred[i, :], 'C0')
plt.fill_between(wpred[i,:], fpred[i,:] + 2 * fpred_err[i,:], \
fpred[i,:] - fpred_err[i,:], color = 'C0', alpha = 0.4, lw = 0)
plt.ylabel('spec. %d' % (i + 1))
plt.xlim(wav.min(), wav.max())
plt.xlabel('wavelength (nm)')
plt.savefig('%s_spectra.png' % prefix)
# Plot the combined spectra with samples from MCMC chain
shifts = np.append(0, MAP_par[:K - 1])
x1d = (x + shifts[:, None]).flatten()
lw1d = (lw1 - lw0) * x1d + lw0
w1d = np.exp(lw1d) * 1e9
y1d = flux.flatten()
y1derr = flux_err.flatten()
inds = np.argsort(x1d)
gp.set_parameter_vector(MAP_par[-2:])
gp.compute(x1d[inds], yerr=y1derr[inds])
fig4 = plt.figure(figsize=(12, nrange + 1))
gs4 = gridspec.GridSpec(nrange, 1)
gs4.update(left=0.1, right=0.98, bottom=0.07, top=0.98, hspace=0.05)
ws = w1d.min()
wr = (w1d.max() - ws) / float(nrange)
for i in range(nrange):
if i == 0:
ax1 = plt.subplot(gs4[0, 0])
else:
axc = plt.subplot(gs4[i, 0], sharey=ax1)
if i < (nrange - 1):
plt.setp(ax1.get_xticklabels(), visible=False)
wmin = ws + (i - 0.05) * wr
wmax = ws + (i + 1.05) * wr
l = (w1d >= wmin) * (w1d <= wmax)
plt.errorbar(w1d[l], y1d[l], yerr = y1derr[l], fmt = ".k", capsize = 0, \
alpha = 0.5, ms = 2, mec='none')
wpred = np.linspace(wmin, wmax, 1000)
lwpred = np.log(wpred * 1e-9)
xpred = (lwpred - lw0) / (lw1 - lw0)
isamp = np.random.randint(nsteps - nburn, size=10)
for j in isamp:
samp_params = samples_flat[j, :].flatten()
samp_shifts = np.append(0, samp_params[:K - 1])
x1_samp = (x + samp_shifts[:, None]).flatten()
inds_samp = np.argsort(x1_samp)
k_samp = terms.Matern32Term(log_sigma=samp_params[-2],
log_rho=samp_params[-1])
gp_samp = GP(k_samp, mean=1.)
gp_samp.compute(x1_samp[inds_samp], yerr=y1derr[inds_samp])
mu, _ = gp.predict(y1d[inds_samp], xpred, return_var=True)
plt.plot(wpred, mu, 'C0-', lw=0.5, alpha=0.5)
plt.xlim(wmin, wmax)
plt.ylabel('flux')
plt.xlabel('wavelength (nm)')
plt.savefig('%s_combined.png' % prefix)
return par_MAP, par50, par50 - par16, par84 - par50, [
fig1, fig2, fig3, fig4
]