def test_confidence_frozen(backend):
dataset = MyDataset()
dataset.parameters["x"].frozen = True
fit = Fit(dataset)
fit.optimize(backend=backend)
result = fit.confidence("y")
assert result["success"] is True
assert_allclose(result["errp"], 1)
assert_allclose(result["errn"], 1)
def test_confidence(backend):
dataset = MyDataset()
fit = Fit(dataset)
fit.optimize(backend=backend)
result = fit.confidence("x")
assert result["success"] is True
assert_allclose(result["errp"], 1)
assert_allclose(result["errn"], 1)
# Check that original value state wasn't changed
assert_allclose(dataset.parameters["x"].value, 2)
def test_minos_contour():
dataset = MyDataset()
dataset.parameters["x"].frozen = True
fit = Fit(dataset)
fit.optimize(backend="minuit")
result = fit.minos_contour("y", "z")
assert result["success"] is True
x = result["x"]
assert_allclose(len(x), 10)
assert_allclose(x[0], 299, rtol=1e-5)
assert_allclose(x[-1], 299.133975, rtol=1e-5)
y = result["y"]
assert_allclose(len(y), 10)
assert_allclose(y[0], 0.04, rtol=1e-5)
assert_allclose(y[-1], 0.54, rtol=1e-5)
# Check that original value state wasn't changed
assert_allclose(dataset.parameters["y"].value, 300)
def test_optimize(backend):
dataset = MyDataset()
fit = Fit(dataset)
result = fit.optimize(backend=backend)
pars = dataset.parameters
assert result.success is True
assert_allclose(result.total_stat, 0)
assert_allclose(pars["x"].value, 2, rtol=1e-3)
assert_allclose(pars["y"].value, 3e2, rtol=1e-3)
assert_allclose(pars["z"].value, 4e-2, rtol=1e-3)
class FluxPointsEstimator:
"""Flux points estimator.
Estimates flux points for a given list of spectral datasets, energies and
spectral model.
To estimate the flux point the amplitude of the reference spectral model is
fitted within the energy range defined by the energy group. This is done for
each group independently. The amplitude is re-normalized using the "norm" parameter,
which specifies the deviation of the flux from the reference model in this
energy group. See https://gamma-astro-data-formats.readthedocs.io/en/latest/spectra/binned_likelihoods/index.html
for details.
The method is also described in the Fermi-LAT catalog paper
https://ui.adsabs.harvard.edu/#abs/2015ApJS..218...23A
or the HESS Galactic Plane Survey paper
https://ui.adsabs.harvard.edu/#abs/2018A%26A...612A...1H
Parameters
----------
datasets : list of `~gammapy.spectrum.SpectrumDatatset`
Spectrum datasets.
e_edges : `~astropy.units.Quantity`
Energy edges of the flux point bins.
source : str
For which source in the model to compute the flux points.
norm_min : float
Minimum value for the norm used for the likelihood profile evaluation.
norm_max : float
Maximum value for the norm used for the likelihood profile evaluation.
norm_n_values : int
Number of norm values used for the likelihood profile.
norm_values : `numpy.ndarray`
Array of norm values to be used for the likelihood profile.
sigma : int
Sigma to use for asymmetric error computation.
sigma_ul : int
Sigma to use for upper limit computation.
reoptimize : bool
Re-optimize other free model parameters.
"""
def __init__(
self,
datasets,
e_edges,
source="",
norm_min=0.2,
norm_max=5,
norm_n_values=11,
norm_values=None,
sigma=1,
sigma_ul=2,
reoptimize=False,
):
# make a copy to not modify the input datasets
if not isinstance(datasets, Datasets):
datasets = Datasets(datasets)
if not datasets.is_all_same_type and datasets.is_all_same_shape:
raise ValueError(
"Flux point estimation requires a list of datasets"
" of the same type and data shape.")
self.datasets = datasets.copy()
self.e_edges = e_edges
dataset = self.datasets.datasets[0]
if isinstance(dataset, SpectrumDatasetOnOff):
model = dataset.model
else:
model = dataset.model[source].spectral_model
self.model = ScaleModel(model)
self.model.norm.min = 0
self.model.norm.max = 1e3
if norm_values is None:
norm_values = np.logspace(np.log10(norm_min), np.log10(norm_max),
norm_n_values)
self.norm_values = norm_values
self.sigma = sigma
self.sigma_ul = sigma_ul
self.reoptimize = reoptimize
self.source = source
self.fit = Fit(self.datasets)
self._set_scale_model()
def _freeze_parameters(self):
# freeze other parameters
for par in self.datasets.parameters:
if par is not self.model.norm:
par.frozen = True
def _freeze_empty_background(self):
from ..cube import MapDataset
counts_all = self.estimate_counts()["counts"]
for counts, dataset in zip(counts_all, self.datasets.datasets):
if isinstance(dataset, MapDataset) and counts == 0:
if dataset.background_model is not None:
dataset.background_model.parameters.freeze_all()
def _set_scale_model(self):
# set the model on all datasets
for dataset in self.datasets.datasets:
if isinstance(dataset, SpectrumDatasetOnOff):
dataset.model = self.model
else:
dataset.model[self.source].spectral_model = self.model
@property
def ref_model(self):
return self.model.model
@property
def e_groups(self):
"""Energy grouping table `~astropy.table.Table`"""
dataset = self.datasets.datasets[0]
if isinstance(dataset, SpectrumDatasetOnOff):
energy_axis = dataset.counts.energy
else:
energy_axis = dataset.counts.geom.get_axis_by_name("energy")
return energy_axis.group_table(self.e_edges)
def __str__(self):
s = "{}:\n".format(self.__class__.__name__)
s += str(self.datasets) + "\n"
s += str(self.e_edges) + "\n"
s += str(self.model) + "\n"
return s
def run(self, steps="all"):
"""Run the flux point estimator for all energy groups.
Returns
-------
flux_points : `FluxPoints`
Estimated flux points.
steps : list of str
Which steps to execute. See `estimate_flux_point` for details
and available options.
"""
rows = []
for e_group in self.e_groups:
if e_group["bin_type"].strip() != "normal":
log.debug(
"Skipping under-/ overflow bin in flux point estimation.")
continue
row = self.estimate_flux_point(e_group, steps=steps)
rows.append(row)
meta = OrderedDict([("SED_TYPE", "likelihood")])
table = table_from_row_data(rows=rows, meta=meta)
return FluxPoints(table).to_sed_type("dnde")
def _energy_mask(self, e_group):
energy_mask = np.zeros(self.datasets.datasets[0].data_shape)
energy_mask[e_group["idx_min"]:e_group["idx_max"] + 1] = 1
return energy_mask.astype(bool)
def estimate_flux_point(self, e_group, steps="all"):
"""Estimate flux point for a single energy group.
Parameters
----------
e_group : `~astropy.table.Row`
Energy group to compute the flux point for.
steps : list of str
Which steps to execute. Available options are:
* "err": estimate symmetric error.
* "errn-errp": estimate asymmetric errors.
* "ul": estimate upper limits.
* "ts": estimate ts and sqrt(ts) values.
* "norm-scan": estimate likelihood profiles.
By default all steps are executed.
Returns
-------
result : dict
Dict with results for the flux point.
"""
e_min, e_max = e_group["energy_min"], e_group["energy_max"]
# Put at log center of the bin
e_ref = np.sqrt(e_min * e_max)
result = OrderedDict([
("e_ref", e_ref),
("e_min", e_min),
("e_max", e_max),
("ref_dnde", self.ref_model(e_ref)),
("ref_flux", self.ref_model.integral(e_min, e_max)),
("ref_eflux", self.ref_model.energy_flux(e_min, e_max)),
("ref_e2dnde", self.ref_model(e_ref) * e_ref**2),
])
contribute_to_likelihood = False
for dataset in self.datasets.datasets:
dataset.mask_fit = self._energy_mask(e_group)
mask = dataset.mask_fit
if dataset.mask_safe is not None:
mask &= dataset.mask_safe
contribute_to_likelihood |= mask.any()
if not contribute_to_likelihood:
raise ValueError(
"No dataset contributes to the likelihood between"
" {e_min:.3f} and {e_max:.3f}. Please adapt the "
"flux point energy edges or check the dataset masks.".format(
e_min=e_min, e_max=e_max))
with self.datasets.parameters.restore_values:
self._freeze_empty_background()
if not self.reoptimize:
self._freeze_parameters()
result.update(self.estimate_norm())
if not result.pop("success"):
log.warning(
"Fit failed for flux point between {e_min:.3f} and {e_max:.3f},"
" setting NaN.".format(e_min=e_min, e_max=e_max))
if steps == "all":
steps = ["err", "counts", "errp-errn", "ul", "ts", "norm-scan"]
if "err" in steps:
result.update(self.estimate_norm_err())
if "counts" in steps:
result.update(self.estimate_counts())
if "errp-errn" in steps:
result.update(self.estimate_norm_errn_errp())
if "ul" in steps:
result.update(self.estimate_norm_ul())
if "ts" in steps:
result.update(self.estimate_norm_ts())
if "norm-scan" in steps:
result.update(self.estimate_norm_scan())
return result
def estimate_norm_errn_errp(self):
"""Estimate asymmetric errors for a flux point.
Returns
-------
result : dict
Dict with asymmetric errors for the flux point norm.
"""
result = self.fit.confidence(parameter=self.model.norm,
sigma=self.sigma)
return {"norm_errp": result["errp"], "norm_errn": result["errn"]}
def estimate_norm_err(self):
"""Estimate covariance errors for a flux point.
Returns
-------
result : dict
Dict with symmetric error for the flux point norm.
"""
result = self.fit.covariance()
norm_err = result.parameters.error(self.model.norm)
return {"norm_err": norm_err}
def estimate_counts(self):
"""Estimate counts for the flux point.
Returns
-------
result : dict
Dict with an array with one entry per dataset with counts for the flux point.
"""
counts = []
for dataset in self.datasets.datasets:
mask = dataset.mask_fit
if dataset.mask_safe is not None:
mask &= dataset.mask_safe
counts.append(dataset.counts.data[mask].sum())
return {"counts": np.array(counts, dtype=int)}
def estimate_norm_ul(self):
"""Estimate upper limit for a flux point.
Returns
-------
result : dict
Dict with upper limit for the flux point norm.
"""
norm = self.model.norm
# TODO: the minuit backend has convergence problems when the likelihood is not
# of parabolic shape, which is the case, when there are zero counts in the
# energy bin. For this case we change to the scipy backend.
counts = self.estimate_counts()["counts"]
if np.all(counts == 0):
result = self.fit.confidence(
parameter=norm,
sigma=self.sigma_ul,
backend="scipy",
reoptimize=self.reoptimize,
)
else:
result = self.fit.confidence(parameter=norm, sigma=self.sigma_ul)
return {"norm_ul": result["errp"] + norm.value}
def estimate_norm_ts(self):
"""Estimate ts and sqrt(ts) for the flux point.
Returns
-------
result : dict
Dict with ts and sqrt(ts) for the flux point.
"""
loglike = self.datasets.likelihood()
# store best fit amplitude, set amplitude of fit model to zero
self.model.norm.value = 0
self.model.norm.frozen = True
if self.reoptimize:
_ = self.fit.optimize()
loglike_null = self.datasets.likelihood()
# compute sqrt TS
ts = np.abs(loglike_null - loglike)
sqrt_ts = np.sqrt(ts)
return {"sqrt_ts": sqrt_ts, "ts": ts}
def estimate_norm_scan(self):
"""Estimate likelihood profile for the norm parameter.
Returns
-------
result : dict
Dict with norm_scan and dloglike_scan for the flux point.
"""
result = self.fit.likelihood_profile(self.model.norm,
values=self.norm_values,
reoptimize=self.reoptimize)
dloglike_scan = result["likelihood"]
return {"norm_scan": result["values"], "dloglike_scan": dloglike_scan}
def estimate_norm(self):
"""Fit norm of the flux point.
Returns
-------
result : dict
Dict with "norm" and "loglike" for the flux point.
"""
# start optimization with norm=1
self.model.norm.value = 1.0
self.model.norm.frozen = False
result = self.fit.optimize()
if result.success:
norm = self.model.norm.value
else:
norm = np.nan
return {
"norm": norm,
"loglike": result.total_stat,
"success": result.success
}
class LightCurveEstimator:
"""Estimate flux points for a given list of datasets, each per time bin.
Parameters
----------
datasets : list of `~gammapy.spectrum.SpectrumDataset` or `~gammapy.cube.MapDataset`
Spectrum or Map datasets.
source : str
For which source in the model to compute the flux points. Default is ''
norm_min : float
Minimum value for the norm used for the likelihood profile evaluation.
norm_max : float
Maximum value for the norm used for the likelihood profile evaluation.
norm_n_values : int
Number of norm values used for the likelihood profile.
norm_values : `numpy.ndarray`
Array of norm values to be used for the likelihood profile.
sigma : int
Sigma to use for asymmetric error computation.
sigma_ul : int
Sigma to use for upper limit computation.
reoptimize : bool
reoptimize other parameters during likelihod scan
"""
def __init__(
self,
datasets,
source="",
norm_min=0.2,
norm_max=5,
norm_n_values=11,
norm_values=None,
sigma=1,
sigma_ul=2,
reoptimize=False,
):
if not isinstance(datasets, Datasets):
datasets = Datasets(datasets)
self.datasets = datasets
if not datasets.is_all_same_type and datasets.is_all_same_shape:
raise ValueError(
"Light Curve estimation requires a list of datasets"
" of the same type and data shape.")
dataset = self.datasets.datasets[0]
if isinstance(dataset, SpectrumDatasetOnOff):
model = dataset.model
else:
model = dataset.model[source].spectral_model
self.model = ScaleModel(model)
self.model.norm.min = 0
self.model.norm.max = 1e5
if norm_values is None:
norm_values = np.logspace(np.log10(norm_min), np.log10(norm_max),
norm_n_values)
self.norm_values = norm_values
self.sigma = sigma
self.sigma_ul = sigma_ul
self.reoptimize = reoptimize
self.source = source
self._set_scale_model()
def _set_scale_model(self):
# set the model on all datasets
for dataset in self.datasets.datasets:
if isinstance(dataset, SpectrumDatasetOnOff):
dataset.model = self.model
else:
dataset.model[self.source].spectral_model = self.model
@property
def ref_model(self):
return self.model.model
def run(self, e_ref, e_min, e_max, steps="all"):
"""Run light curve extraction.
Normalize integral and energy flux between emin and emax.
Parameters
----------
e_ref : `~astropy.unit.Quantity`
reference energy of dnde flux normalization
e_min : `~astropy.unit.Quantity`
minimum energy of integral and energy flux normalization interval
e_max : `~astropy.unit.Quantity`
minimum energy of integral and energy flux normalization interval
steps : list of str
Which steps to execute. Available options are:
* "err": estimate symmetric error.
* "errn-errp": estimate asymmetric errors.
* "ul": estimate upper limits.
* "ts": estimate ts and sqrt(ts) values.
* "norm-scan": estimate likelihood profiles.
By default all steps are executed.
Returns
-------
lightcurve : `~gammapy.time.LightCurve`
the Light Curve object
"""
self.e_ref = e_ref
self.e_min = e_min
self.e_max = e_max
rows = []
for dataset in self.datasets.datasets:
row = {
"time_min": dataset.counts.meta["t_start"].mjd,
"time_max": dataset.counts.meta["t_stop"].mjd,
}
row.update(self.estimate_time_bin_flux(dataset, steps))
rows.append(row)
meta = OrderedDict([("SED_TYPE", "likelihood")])
table = table_from_row_data(rows=rows, meta=meta)
table = FluxPoints(table).to_sed_type("flux").table
return LightCurve(table)
def estimate_time_bin_flux(self, dataset, steps="all"):
"""Estimate flux point for a single energy group.
Parameters
----------
steps : list of str
Which steps to execute. Available options are:
* "err": estimate symmetric error.
* "errn-errp": estimate asymmetric errors.
* "ul": estimate upper limits.
* "ts": estimate ts and sqrt(ts) values.
* "norm-scan": estimate likelihood profiles.
By default all steps are executed.
Returns
-------
result : dict
Dict with results for the flux point.
"""
self.fit = Fit(dataset)
result = OrderedDict([
("e_ref", self.e_ref),
("e_min", self.e_min),
("e_max", self.e_max),
("ref_dnde", self.ref_model(self.e_ref)),
("ref_flux", self.ref_model.integral(self.e_min, self.e_max)),
("ref_eflux", self.ref_model.energy_flux(self.e_min, self.e_max)),
("ref_e2dnde", self.ref_model(self.e_ref) * self.e_ref**2),
])
result.update(self.estimate_norm())
if not result.pop("success"):
log.warning("Fit failed for time bin between {t_min} and {t_max},"
" setting NaN.".format(
t_min=dataset.counts.meta["t_start"],
t_max=dataset.counts.meta["t_stop"],
))
if steps == "all":
steps = ["err", "counts", "errp-errn", "ul", "ts", "norm-scan"]
if "err" in steps:
result.update(self.estimate_norm_err())
if "counts" in steps:
result.update(self.estimate_counts(dataset))
if "errp-errn" in steps:
result.update(self.estimate_norm_errn_errp())
if "ul" in steps:
result.update(self.estimate_norm_ul(dataset))
if "ts" in steps:
result.update(self.estimate_norm_ts())
if "norm-scan" in steps:
result.update(self.estimate_norm_scan())
return result
# TODO : most of the following code is copied from FluxPointsEstimator, can it be restructured?
def estimate_norm_errn_errp(self):
"""Estimate asymmetric errors for a flux point.
Returns
-------
result : dict
Dict with asymmetric errors for the flux point norm.
"""
result = self.fit.confidence(parameter=self.model.norm,
sigma=self.sigma)
return {"norm_errp": result["errp"], "norm_errn": result["errn"]}
def estimate_norm_err(self):
"""Estimate covariance errors for a flux point.
Returns
-------
result : dict
Dict with symmetric error for the flux point norm.
"""
result = self.fit.covariance()
norm_err = result.parameters.error(self.model.norm)
return {"norm_err": norm_err}
def estimate_counts(self, dataset):
"""Estimate counts for the flux point.
Parameters
----------
dataset : `~gammapy.utils.fitting.Dataset`
the dataset object
Returns
-------
result : dict
Dict with an array with one entry per dataset with counts for the flux point.
"""
# TODO : use e_min and e_max interval for counts calculation
# TODO : add off counts and excess? for DatasetOnOff
# TODO : this may require a loop once we support Datasets per time bin
mask = dataset.mask
if dataset.mask_safe is not None:
mask &= dataset.mask_safe
counts = dataset.counts.data[mask].sum()
return {"counts": counts}
def estimate_norm_ul(self, dataset):
"""Estimate upper limit for a flux point.
Returns
-------
result : dict
Dict with upper limit for the flux point norm.
"""
norm = self.model.norm
# TODO: the minuit backend has convergence problems when the likelihood is not
# of parabolic shape, which is the case, when there are zero counts in the
# bin. For this case we change to the scipy backend.
counts = self.estimate_counts(dataset)["counts"]
if np.all(counts == 0):
result = self.fit.confidence(
parameter=norm,
sigma=self.sigma_ul,
backend="scipy",
reoptimize=self.reoptimize,
)
else:
result = self.fit.confidence(parameter=norm, sigma=self.sigma_ul)
return {"norm_ul": result["errp"] + norm.value}
def estimate_norm_ts(self):
"""Estimate ts and sqrt(ts) for the flux point.
Returns
-------
result : dict
Dict with ts and sqrt(ts) for the flux point.
"""
loglike = self.datasets.likelihood()
# store best fit amplitude, set amplitude of fit model to zero
self.model.norm.value = 0
self.model.norm.frozen = True
if self.reoptimize:
_ = self.fit.optimize()
loglike_null = self.datasets.likelihood()
# compute sqrt TS
ts = np.abs(loglike_null - loglike)
sqrt_ts = np.sqrt(ts)
return {"sqrt_ts": sqrt_ts, "ts": ts}
def estimate_norm_scan(self):
"""Estimate likelihood profile for the norm parameter.
Returns
-------
result : dict
Dict with norm_scan and dloglike_scan for the flux point.
"""
result = self.fit.likelihood_profile(self.model.norm,
values=self.norm_values,
reoptimize=self.reoptimize)
dloglike_scan = result["likelihood"]
return {"norm_scan": result["values"], "dloglike_scan": dloglike_scan}
def estimate_norm(self):
"""Fit norm of the flux point.
Returns
-------
result : dict
Dict with "norm" and "loglike" for the flux point.
"""
# start optimization with norm=1
self.model.norm.value = 1.0
self.model.norm.frozen = False
result = self.fit.optimize()
if result.success:
norm = self.model.norm.value
else:
norm = np.nan
return {
"norm": norm,
"loglike": result.total_stat,
"success": result.success
}