# Licensed under a 3-clause BSD style license - see LICENSE.rst
import logging
from collections import OrderedDict
import numpy as np
from astropy.table import Table, vstack
from astropy import units as u
from astropy.io.registry import IORegistryError
from ..utils.scripts import make_path
from ..utils.table import table_standardise_units_copy, table_from_row_data
from ..utils.interpolation import interpolate_likelihood_profile
from ..utils.fitting import Dataset, Datasets, Fit
from .models import PowerLaw, ScaleModel
from .powerlaw import power_law_integral_flux
from .dataset import SpectrumDatasetOnOff
__all__ = ["FluxPoints", "FluxPointsEstimator", "FluxPointsDataset"]
log = logging.getLogger(__name__)
REQUIRED_COLUMNS = OrderedDict(
[
("dnde", ["e_ref", "dnde"]),
("e2dnde", ["e_ref", "e2dnde"]),
("flux", ["e_min", "e_max", "flux"]),
("eflux", ["e_min", "e_max", "eflux"]),
# TODO: extend required columns
(
"likelihood",
[
"e_min",
"e_max",
"e_ref",
"ref_dnde",
"norm",
"norm_scan",
"dloglike_scan",
],
),
]
)
OPTIONAL_COLUMNS = OrderedDict(
[
("dnde", ["dnde_err", "dnde_errp", "dnde_errn", "dnde_ul", "is_ul"]),
("e2dnde", ["e2dnde_err", "e2dnde_errp", "e2dnde_errn", "e2dnde_ul", "is_ul"]),
("flux", ["flux_err", "flux_errp", "flux_errn", "flux_ul", "is_ul"]),
("eflux", ["eflux_err", "eflux_errp", "eflux_errn", "eflux_ul", "is_ul"]),
]
)
DEFAULT_UNIT = OrderedDict(
[
("dnde", u.Unit("cm-2 s-1 TeV-1")),
("e2dnde", u.Unit("erg cm-2 s-1")),
("flux", u.Unit("cm-2 s-1")),
("eflux", u.Unit("erg cm-2 s-1")),
]
)
[docs]class FluxPoints:
"""Flux points container.
The supported formats are described here: :ref:`gadf:flux-points`
In summary, the following formats and minimum required columns are:
* Format ``dnde``: columns ``e_ref`` and ``dnde``
* Format ``e2dnde``: columns ``e_ref``, ``e2dnde``
* Format ``flux``: columns ``e_min``, ``e_max``, ``flux``
* Format ``eflux``: columns ``e_min``, ``e_max``, ``eflux``
Parameters
----------
table : `~astropy.table.Table`
Table with flux point data
Attributes
----------
table : `~astropy.table.Table`
Table with flux point data
Examples
--------
The `FluxPoints` object is most easily created by reading a file with
flux points given in one of the formats documented above::
from gammapy.spectrum import FluxPoints
filename = '$GAMMAPY_DATA/tests/spectrum/flux_points/flux_points.fits'
flux_points = FluxPoints.read(filename)
flux_points.plot()
An instance of `FluxPoints` can also be created by passing an instance of
`astropy.table.Table`, which contains the required columns, such as `'e_ref'`
and `'dnde'`. The corresponding `sed_type` has to be defined in the meta data
of the table::
from astropy import units as u
from astropy.table import Table
from gammapy.spectrum import FluxPoints
from gammapy.spectrum.models import PowerLaw
table = Table()
pwl = PowerLaw()
e_ref = np.logspace(0, 2, 7) * u.TeV
table['e_ref'] = e_ref
table['dnde'] = pwl(e_ref)
table.meta['SED_TYPE'] = 'dnde'
flux_points = FluxPoints(table)
flux_points.plot()
If you have flux points in a different data format, the format can be changed
by renaming the table columns and adding meta data::
from astropy import units as u
from astropy.table import Table
from gammapy.spectrum import FluxPoints
table = Table.read('$GAMMAPY_DATA/tests/spectrum/flux_points/flux_points_ctb_37b.txt',
format='ascii.csv', delimiter=' ', comment='#')
table.meta['SED_TYPE'] = 'dnde'
table.rename_column('Differential_Flux', 'dnde')
table['dnde'].unit = 'cm-2 s-1 TeV-1'
table.rename_column('lower_error', 'dnde_errn')
table['dnde_errn'].unit = 'cm-2 s-1 TeV-1'
table.rename_column('upper_error', 'dnde_errp')
table['dnde_errp'].unit = 'cm-2 s-1 TeV-1'
table.rename_column('E', 'e_ref')
table['e_ref'].unit = 'TeV'
flux_points = FluxPoints(table)
flux_points.plot()
"""
def __init__(self, table):
self.table = table_standardise_units_copy(table)
# validate that the table is a valid representation
# of the given flux point sed type
self._validate_table(self.table, table.meta["SED_TYPE"])
def __repr__(self):
fmt = '{}(sed_type="{}", n_points={})'
return fmt.format(self.__class__.__name__, self.sed_type, len(self.table))
@property
def table_formatted(self):
"""Return formatted version of the flux points table. Used for pretty printing"""
table = self.table.copy()
for column in table.colnames:
if column.startswith(("dnde", "eflux", "flux", "e2dnde", "ref")):
table[column].format = ".3e"
elif column.startswith(
("e_min", "e_max", "e_ref", "sqrt_ts", "norm", "ts", "loglike")
):
table[column].format = ".3f"
return table
[docs] @classmethod
def read(cls, filename, **kwargs):
"""Read flux points.
Parameters
----------
filename : str
Filename
kwargs : dict
Keyword arguments passed to `astropy.table.Table.read`.
"""
filename = make_path(filename)
try:
table = Table.read(str(filename), **kwargs)
except IORegistryError:
kwargs.setdefault("format", "ascii.ecsv")
table = Table.read(str(filename), **kwargs)
if "SED_TYPE" not in table.meta.keys():
sed_type = cls._guess_sed_type(table)
table.meta["SED_TYPE"] = sed_type
return cls(table=table)
[docs] def write(self, filename, **kwargs):
"""Write flux points.
Parameters
----------
filename : str
Filename
kwargs : dict
Keyword arguments passed to `astropy.table.Table.write`.
"""
filename = make_path(filename)
try:
self.table.write(str(filename), **kwargs)
except IORegistryError:
kwargs.setdefault("format", "ascii.ecsv")
self.table.write(str(filename), **kwargs)
[docs] @classmethod
def stack(cls, flux_points):
"""Create flux points by stacking list of flux points.
The first `FluxPoints` object in the list is taken as a reference to infer
column names and units for the stacked object.
Parameters
----------
flux_points : list of `FluxPoints`
List of flux points to stack.
Returns
-------
flux_points : `FluxPoints`
Flux points without upper limit points.
"""
reference = flux_points[0].table
tables = []
for _ in flux_points:
table = _.table
for colname in reference.colnames:
column = reference[colname]
if column.unit:
table[colname] = table[colname].quantity.to(column.unit)
tables.append(table[reference.colnames])
table_stacked = vstack(tables)
table_stacked.meta["SED_TYPE"] = reference.meta["SED_TYPE"]
return cls(table_stacked)
[docs] def drop_ul(self):
"""Drop upper limit flux points.
Returns
-------
flux_points : `FluxPoints`
Flux points with upper limit points removed.
Examples
--------
>>> from gammapy.spectrum import FluxPoints
>>> filename = '$GAMMAPY_DATA/tests/spectrum/flux_points/flux_points.fits'
>>> flux_points = FluxPoints.read(filename)
>>> print(flux_points)
FluxPoints(sed_type="flux", n_points=24)
>>> print(flux_points.drop_ul())
FluxPoints(sed_type="flux", n_points=19)
"""
table_drop_ul = self.table[~self.is_ul]
return self.__class__(table_drop_ul)
def _flux_to_dnde(self, e_ref, table, model, pwl_approx):
if model is None:
model = PowerLaw()
e_min, e_max = self.e_min, self.e_max
flux = table["flux"].quantity
dnde = self._dnde_from_flux(flux, model, e_ref, e_min, e_max, pwl_approx)
# Add to result table
table["e_ref"] = e_ref
table["dnde"] = dnde
if "flux_err" in table.colnames:
table["dnde_err"] = dnde * table["flux_err"].quantity / flux
if "flux_errn" in table.colnames:
table["dnde_errn"] = dnde * table["flux_errn"].quantity / flux
table["dnde_errp"] = dnde * table["flux_errp"].quantity / flux
if "flux_ul" in table.colnames:
flux_ul = table["flux_ul"].quantity
dnde_ul = self._dnde_from_flux(
flux_ul, model, e_ref, e_min, e_max, pwl_approx
)
table["dnde_ul"] = dnde_ul
return table
@staticmethod
def _dnde_to_e2dnde(e_ref, table):
for suffix in ["", "_ul", "_err", "_errp", "_errn"]:
try:
data = table["dnde" + suffix].quantity
table["e2dnde" + suffix] = (e_ref ** 2 * data).to(
DEFAULT_UNIT["e2dnde"]
)
except KeyError:
continue
return table
@staticmethod
def _e2dnde_to_dnde(e_ref, table):
for suffix in ["", "_ul", "_err", "_errp", "_errn"]:
try:
data = table["e2dnde" + suffix].quantity
table["dnde" + suffix] = (data / e_ref ** 2).to(DEFAULT_UNIT["dnde"])
except KeyError:
continue
return table
[docs] def to_sed_type(self, sed_type, method="log_center", model=None, pwl_approx=False):
"""Convert to a different SED type (return new `FluxPoints`).
See: http://adsabs.harvard.edu/abs/1995NIMPA.355..541L for details
on the `'lafferty'` method.
Parameters
----------
sed_type : {'dnde'}
SED type to convert to.
model : `~gammapy.spectrum.models.SpectralModel`
Spectral model assumption. Note that the value of the amplitude parameter
does not matter. Still it is recommended to use something with the right
scale and units. E.g. `amplitude = 1e-12 * u.Unit('cm-2 s-1 TeV-1')`
method : {'lafferty', 'log_center', 'table'}
Flux points `e_ref` estimation method:
* `'laferty'` Lafferty & Wyatt model-based e_ref
* `'log_center'` log bin center e_ref
* `'table'` using column 'e_ref' from input flux_points
pwl_approx : bool
Use local power law appoximation at e_ref to compute differential flux
from the integral flux. This method is used by the Fermi-LAT catalogs.
Returns
-------
flux_points : `FluxPoints`
Flux points including differential quantity columns `dnde`
and `dnde_err` (optional), `dnde_ul` (optional).
Examples
--------
>>> from gammapy.spectrum import FluxPoints
>>> from gammapy.spectrum.models import PowerLaw
>>> filename = '$GAMMAPY_DATA/tests/spectrum/flux_points/flux_points.fits'
>>> flux_points = FluxPoints.read(filename)
>>> model = PowerLaw(index=2.2)
>>> flux_points_dnde = flux_points.to_sed_type('dnde', model=model)
"""
# TODO: implement other directions.
table = self.table.copy()
if self.sed_type == "flux" and sed_type == "dnde":
# Compute e_ref
if method == "table":
e_ref = table["e_ref"].quantity
elif method == "log_center":
e_ref = np.sqrt(self.e_min * self.e_max)
elif method == "lafferty":
# set e_ref that it represents the mean dnde in the given energy bin
e_ref = self._e_ref_lafferty(model, self.e_min, self.e_max)
else:
raise ValueError("Invalid method: {}".format(method))
table = self._flux_to_dnde(e_ref, table, model, pwl_approx)
elif self.sed_type == "dnde" and sed_type == "e2dnde":
table = self._dnde_to_e2dnde(self.e_ref, table)
elif self.sed_type == "e2dnde" and sed_type == "dnde":
table = self._e2dnde_to_dnde(self.e_ref, table)
elif self.sed_type == "likelihood" and sed_type in ["dnde", "flux", "eflux"]:
for suffix in ["", "_ul", "_err", "_errp", "_errn"]:
try:
table[sed_type + suffix] = (
table["ref_" + sed_type] * table["norm" + suffix]
)
except KeyError:
continue
else:
raise NotImplementedError
table.meta["SED_TYPE"] = sed_type
return FluxPoints(table)
@staticmethod
def _e_ref_lafferty(model, e_min, e_max):
"""Helper for `to_sed_type`.
Compute e_ref that the value at e_ref corresponds
to the mean value between e_min and e_max.
"""
flux = model.integral(e_min, e_max)
dnde_mean = flux / (e_max - e_min)
return model.inverse(dnde_mean)
@staticmethod
def _dnde_from_flux(flux, model, e_ref, e_min, e_max, pwl_approx):
"""Helper for `to_sed_type`.
Compute dnde under the assumption that flux equals expected
flux from model.
"""
dnde_model = model(e_ref)
if pwl_approx:
index = model.spectral_index(e_ref)
flux_model = power_law_integral_flux(
f=dnde_model, g=index, e=e_ref, e1=e_min, e2=e_max
)
else:
flux_model = model.integral(e_min, e_max, intervals=True)
return dnde_model * (flux / flux_model)
@property
def sed_type(self):
"""SED type (str).
One of: {'dnde', 'e2dnde', 'flux', 'eflux'}
"""
return self.table.meta["SED_TYPE"]
@staticmethod
def _guess_sed_type(table):
"""Guess SED type from table content."""
valid_sed_types = list(REQUIRED_COLUMNS.keys())
for sed_type in valid_sed_types:
required = set(REQUIRED_COLUMNS[sed_type])
if required.issubset(table.colnames):
return sed_type
@staticmethod
def _guess_sed_type_from_unit(unit):
"""Guess SED type from unit."""
for sed_type, default_unit in DEFAULT_UNIT.items():
if unit.is_equivalent(default_unit):
return sed_type
@staticmethod
def _validate_table(table, sed_type):
"""Validate input table."""
required = set(REQUIRED_COLUMNS[sed_type])
if not required.issubset(table.colnames):
missing = required.difference(table.colnames)
raise ValueError(
"Missing columns for sed type '{}':" " {}".format(sed_type, missing)
)
@staticmethod
def _get_y_energy_unit(y_unit):
"""Get energy part of the given y unit."""
try:
return [_ for _ in y_unit.bases if _.physical_type == "energy"][0]
except IndexError:
return u.Unit("TeV")
def _plot_get_energy_err(self):
"""Compute energy error for given sed type"""
try:
e_min = self.table["e_min"].quantity
e_max = self.table["e_max"].quantity
e_ref = self.e_ref
x_err = ((e_ref - e_min), (e_max - e_ref))
except KeyError:
x_err = None
return x_err
def _plot_get_flux_err(self, sed_type=None):
"""Compute flux error for given sed type"""
try:
# asymmetric error
y_errn = self.table[sed_type + "_errn"].quantity
y_errp = self.table[sed_type + "_errp"].quantity
y_err = (y_errn, y_errp)
except KeyError:
try:
# symmetric error
y_err = self.table[sed_type + "_err"].quantity
y_err = (y_err, y_err)
except KeyError:
# no error at all
y_err = None
return y_err
@property
def is_ul(self):
try:
return self.table["is_ul"].data.astype("bool")
except KeyError:
return np.isnan(self.table[self.sed_type])
@property
def e_ref(self):
"""Reference energy.
Defined by `e_ref` column in `FluxPoints.table` or computed as log
center, if `e_min` and `e_max` columns are present in `FluxPoints.table`.
Returns
-------
e_ref : `~astropy.units.Quantity`
Reference energy.
"""
try:
return self.table["e_ref"].quantity
except KeyError:
return np.sqrt(self.e_min * self.e_max)
@property
def e_edges(self):
"""Edges of the energy bin.
Returns
-------
e_edges : `~astropy.units.Quantity`
Energy edges.
"""
e_edges = list(self.e_min)
e_edges += [self.e_max[-1]]
return u.Quantity(e_edges, self.e_min.unit, copy=False)
@property
def e_min(self):
"""Lower bound of energy bin.
Defined by `e_min` column in `FluxPoints.table`.
Returns
-------
e_min : `~astropy.units.Quantity`
Lower bound of energy bin.
"""
return self.table["e_min"].quantity
@property
def e_max(self):
"""Upper bound of energy bin.
Defined by ``e_max`` column in ``table``.
Returns
-------
e_max : `~astropy.units.Quantity`
Upper bound of energy bin.
"""
return self.table["e_max"].quantity
[docs] def plot(
self, ax=None, energy_unit="TeV", flux_unit=None, energy_power=0, **kwargs
):
"""Plot flux points.
Parameters
----------
ax : `~matplotlib.axes.Axes`
Axis object to plot on.
energy_unit : str, `~astropy.units.Unit`, optional
Unit of the energy axis
flux_unit : str, `~astropy.units.Unit`, optional
Unit of the flux axis
energy_power : int
Power of energy to multiply y axis with
kwargs : dict
Keyword arguments passed to :func:`matplotlib.pyplot.errorbar`
Returns
-------
ax : `~matplotlib.axes.Axes`
Axis object
"""
import matplotlib.pyplot as plt
if ax is None:
ax = plt.gca()
sed_type = self.sed_type
y_unit = u.Unit(flux_unit or DEFAULT_UNIT[sed_type])
y = self.table[sed_type].quantity.to(y_unit)
x = self.e_ref.to(energy_unit)
# get errors and ul
is_ul = self.is_ul
x_err_all = self._plot_get_energy_err()
y_err_all = self._plot_get_flux_err(sed_type)
# handle energy power
e_unit = self._get_y_energy_unit(y_unit)
y_unit = y.unit * e_unit ** energy_power
y = (y * np.power(x, energy_power)).to(y_unit)
y_err, x_err = None, None
if y_err_all:
y_errn = (y_err_all[0] * np.power(x, energy_power)).to(y_unit)
y_errp = (y_err_all[1] * np.power(x, energy_power)).to(y_unit)
y_err = (y_errn[~is_ul].to_value(y_unit), y_errp[~is_ul].to_value(y_unit))
if x_err_all:
x_errn, x_errp = x_err_all
x_err = (
x_errn[~is_ul].to_value(energy_unit),
x_errp[~is_ul].to_value(energy_unit),
)
# set flux points plotting defaults
kwargs.setdefault("marker", "+")
kwargs.setdefault("ls", "None")
ebar = ax.errorbar(
x[~is_ul].value, y[~is_ul].value, yerr=y_err, xerr=x_err, **kwargs
)
if is_ul.any():
if x_err_all:
x_errn, x_errp = x_err_all
x_err = (
x_errn[is_ul].to_value(energy_unit),
x_errp[is_ul].to_value(energy_unit),
)
y_ul = self.table[sed_type + "_ul"].quantity
y_ul = (y_ul * np.power(x, energy_power)).to(y_unit)
y_err = (0.5 * y_ul[is_ul].value, np.zeros_like(y_ul[is_ul].value))
kwargs.setdefault("color", ebar[0].get_color())
# pop label keyword to avoid that it appears twice in the legend
kwargs.pop("label", None)
ax.errorbar(
x[is_ul].value,
y_ul[is_ul].value,
xerr=x_err,
yerr=y_err,
uplims=True,
**kwargs
)
ax.set_xscale("log", nonposx="clip")
ax.set_yscale("log", nonposy="clip")
ax.set_xlabel("Energy ({})".format(energy_unit))
ax.set_ylabel("{} ({})".format(self.sed_type, y_unit))
return ax
[docs] def plot_likelihood(
self,
ax=None,
energy_unit="TeV",
add_cbar=True,
y_values=None,
y_unit=None,
**kwargs
):
"""Plot likelihood SED profiles as a density plot..
Parameters
----------
ax : `~matplotlib.axes.Axes`
Axis object to plot on.
energy_unit : str, `~astropy.units.Unit`, optional
Unit of the energy axis
y_values : `astropy.units.Quantity`
Array of y-values to use for the likelihood profile evaluation.
y_unit : str or `astropy.units.Unit`
Unit to use for the y-axis.
add_cbar : bool
Whether to add a colorbar to the plot.
kwargs : dict
Keyword arguments passed to :func:`matplotlib.pyplot.pcolormesh`
Returns
-------
ax : `~matplotlib.axes.Axes`
Axis object
"""
import matplotlib.pyplot as plt
if ax is None:
ax = plt.gca()
self._validate_table(self.table, "likelihood")
y_unit = u.Unit(y_unit or DEFAULT_UNIT[self.sed_type])
if y_values is None:
ref_values = self.table["ref_" + self.sed_type].quantity
y_values = np.logspace(
np.log10(0.2 * ref_values.value.min()),
np.log10(5 * ref_values.value.max()),
500,
)
y_values = u.Quantity(y_values, y_unit, copy=False)
x = self.e_edges.to(energy_unit)
# Compute likelihood "image" one energy bin at a time
# by interpolating e2dnde at the log bin centers
z = np.empty((len(self.table), len(y_values)))
for idx, row in enumerate(self.table):
y_ref = self.table["ref_" + self.sed_type].quantity[idx]
norm = (y_values / y_ref).to_value("")
norm_scan = row["norm_scan"]
dloglike_scan = row["dloglike_scan"] - row["loglike"]
interp = interpolate_likelihood_profile(norm_scan, dloglike_scan)
z[idx] = interp((norm,))
kwargs.setdefault("vmax", 0)
kwargs.setdefault("vmin", -4)
kwargs.setdefault("zorder", 0)
kwargs.setdefault("cmap", "Blues")
kwargs.setdefault("linewidths", 0)
# clipped values are set to NaN so that they appear white on the plot
z[-z < kwargs["vmin"]] = np.nan
caxes = ax.pcolormesh(x, y_values, -z.T, **kwargs)
ax.set_xscale("log", nonposx="clip")
ax.set_yscale("log", nonposy="clip")
ax.set_xlabel("Energy ({})".format(energy_unit))
ax.set_ylabel("{} ({})".format(self.sed_type, y_values.unit))
if add_cbar:
label = "delta log-likelihood"
ax.figure.colorbar(caxes, ax=ax, label=label)
return ax
[docs]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
[docs] 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)
[docs] 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
[docs] 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"]}
[docs] 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}
[docs] 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
if isinstance(dataset, SpectrumDatasetOnOff):
counts.append(dataset.counts.data.data[mask].sum())
else:
counts.append(dataset.counts.data[mask].sum())
return {"counts": np.array(counts, dtype=int)}
[docs] 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}
[docs] 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}
[docs] 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}
[docs] 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}
[docs]class FluxPointsDataset(Dataset):
"""
Fit a set of flux points with a parametric model.
Parameters
----------
model : `~gammapy.spectrum.models.SpectralModel`
Spectral model
data : `~gammapy.spectrum.FluxPoints`
Flux points.
mask_fit : `numpy.ndarray`
Mask to apply to the likelihood for fitting.
likelihood : {"chi2", "chi2assym"}
Likelihood function to use for the fit.
mask_safe : `numpy.ndarray`
Mask defining the safe data range.
Examples
--------
Load flux points from file and fit with a power-law model::
from astropy import units as u
from gammapy.spectrum import FluxPoints, FluxPointsDataset
from gammapy.utils.fitting import Fit
from gammapy.spectrum.models import PowerLaw
filename = '$GAMMAPY_DATA/tests/spectrum/flux_points/diff_flux_points.fits'
flux_points = FluxPoints.read(filename)
model = PowerLaw()
dataset = FluxPointsDataset(model, flux_points)
fit = Fit(dataset)
result = fit.run()
print(result)
print(result.parameters.to_table())
"""
def __init__(self, model, data, mask_fit=None, likelihood="chi2", mask_safe=None):
self.model = model
self.data = data
self.mask_fit = mask_fit
self.parameters = model.parameters
if data.sed_type != "dnde":
raise ValueError("Currently only flux points of type 'dnde' are supported.")
if mask_safe is None:
mask_safe = np.isfinite(data.table["dnde"])
self.mask_safe = mask_safe
if likelihood in ["chi2", "chi2assym"]:
self._likelihood = likelihood
else:
raise ValueError(
"'{likelihood}' is not a valid fit statistic, please choose"
" either 'chi2' or 'chi2assym'"
)
[docs] def data_shape(self):
"""Shape of the flux points data"""
return self.data.e_ref.shape
@staticmethod
def _likelihood_chi2(data, model, sigma):
return ((data - model) / sigma).to_value("") ** 2
@staticmethod
def _likelihood_chi2_assym(data, model, sigma_n, sigma_p):
"""
Assymetric chi2 statistics for a list of flux points and model.
"""
is_p = model > data
sigma = sigma_n
sigma[is_p] = sigma_p[is_p]
return FluxPointsDataset._likelihood_chi2(data, model, sigma)
[docs] def flux_pred(self):
"""Compute predicted flux."""
return self.model(self.data.e_ref)
[docs] def likelihood_per_bin(self):
"""Likelihood per bin given the current model parameters"""
model = self.flux_pred()
data = self.data.table["dnde"].quantity
if self._likelihood == "chi2":
sigma = self.data.table["dnde_err"].quantity
return self._likelihood_chi2(data, model, sigma)
elif self._likelihood == "chi2assym":
sigma_n = self.data.table["dnde_errn"].quantity
sigma_p = self.data.table["dnde_errp"].quantity
return self._likelihood_chi2_assym(data, model, sigma_n, sigma_p)
else:
# TODO: add likelihood profiles
pass
[docs] def residuals(self):
"""Compute flux point residuals
Defined as `(data - model) / model`.
Returns
-------
residuals : `~numpy.ndarray`
Flux point residuals
"""
fp = self.data
data = fp.table[fp.sed_type].quantity
model = self.model(fp.e_ref)
residuals = ((data - model) / model).to_value("")
# Remove residuals for upper_limits
residuals[fp.is_ul] = np.nan
return residuals
[docs] def peek(self, **kwargs):
"""Plot flux points, best fit model and residuals.
"""
from matplotlib.gridspec import GridSpec
import matplotlib.pyplot as plt
gs = GridSpec(7, 1)
ax_spectrum = plt.subplot(gs[:5, :])
self.plot_spectrum(ax=ax_spectrum, **kwargs)
ax_spectrum.set_xticks([])
ax_residuals = plt.subplot(gs[5:, :])
self.plot_residuals(ax=ax_residuals)
return ax_spectrum, ax_residuals
@property
def _e_range(self):
try:
return u.Quantity([self.data.e_min.min(), self.data.e_max.max()])
except KeyError:
return u.Quantity([self.data.e_ref.min(), self.data.e_ref.max()])
@property
def _e_unit(self):
return self.data.e_ref.unit
[docs] def plot_residuals(self, ax=None, **kwargs):
"""Plot flux point residuals.
Parameters
----------
ax : `~matplotlib.pyplot.Axes`
Axes object.
**kwargs : dict
Keyword arguments passed to `~matplotlib.pyplot.errorbar`.
Returns
-------
ax : `~matplotlib.pyplot.Axes`
Axes object.
"""
import matplotlib.pyplot as plt
ax = plt.gca() if ax is None else ax
residuals = self.residuals()
fp = self.data
xerr = fp._plot_get_energy_err()
if xerr is not None:
xerr = xerr[0].to_value(self._e_unit), xerr[1].to_value(self._e_unit)
model = self.model(fp.e_ref)
yerr = fp._plot_get_flux_err(fp.sed_type)
yerr = (yerr[0] / model).to_value(""), (yerr[1] / model).to_value("")
kwargs.setdefault("marker", "+")
kwargs.setdefault("ls", "None")
ax.errorbar(self.data.e_ref.value, residuals, xerr=xerr, yerr=yerr, **kwargs)
# format axes
ax.axhline(0, color="black", lw=0.5)
ax.set_ylabel("Residuals")
ax.set_xlabel("Energy ({})".format(self._e_unit))
ax.set_ylim(-1, 1)
ax.set_xscale("log")
ax.set_xlim(self._e_range.to_value(self._e_unit))
return ax
[docs] def plot_spectrum(self, ax=None, fp_kwargs=None, model_kwargs=None):
"""
Plot spectrum including flux points and model.
Parameters
----------
ax : `~matplotlib.pyplot.Axes`
Axes object.
fp_kwargs : dict
Keyword arguments passed to `FluxPoints.plot`.
model_kwargs : dict
Keywords passed to `SpectralModel.plot` and `SpectralModel.plot_error`
Returns
-------
ax : `~matplotlib.pyplot.Axes`
Axes object.
"""
import matplotlib.pyplot as plt
ax = plt.gca() if ax is None else ax
fp_kwargs = {} if fp_kwargs is None else fp_kwargs
model_kwargs = {} if model_kwargs is None else model_kwargs
kwargs = {}
kwargs.setdefault("flux_unit", "erg-1 cm-2 s-1")
kwargs.setdefault("energy_unit", "TeV")
kwargs.setdefault("energy_power", 2)
# plot flux points
plot_kwargs = kwargs.copy()
plot_kwargs.update(fp_kwargs)
plot_kwargs.setdefault("label", "Flux points")
ax = self.data.plot(ax=ax, **plot_kwargs)
plot_kwargs = kwargs.copy()
plot_kwargs.setdefault("energy_range", self._e_range)
plot_kwargs.setdefault("zorder", 10)
plot_kwargs.update(model_kwargs)
plot_kwargs.setdefault("label", "Best fit model")
self.model.plot(ax=ax, **plot_kwargs)
plot_kwargs.setdefault("color", ax.lines[-1].get_color())
del plot_kwargs["label"]
if self.model.parameters.covariance is not None:
self.model.plot_error(ax=ax, **plot_kwargs)
# format axes
ax.set_xlim(self._e_range.to_value(self._e_unit))
return ax