Source code for gammapy.spectrum.flux_point

# Licensed under a 3-clause BSD style license - see LICENSE.rst
from __future__ import absolute_import, division, print_function, unicode_literals
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.fitting import Fit
from ..utils.interpolation import ScaledRegularGridInterpolator
from .models import PowerLaw, ScaleModel
from .powerlaw import power_law_integral_flux
from .observation import SpectrumObservationList, SpectrumObservation

__all__ = ["FluxPoints", "FluxPointEstimator", "FluxPointFit"]

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")),
    ]
)


def _interp_likelihood_profile(norm_scan, dloglike_scan, norm):
    """Helper function to interpolate likelihood profiles"""
    # likelihood profiles are typically of parabolic shape, so we use a
    # sqrt scaling of the values and perform linear interpolation on the scaled
    # values
    sign = np.sign(np.gradient(dloglike_scan))
    interp = ScaledRegularGridInterpolator(
        points=(norm_scan,), values=sign * dloglike_scan, values_scale="sqrt"
    )
    return interp((norm,))


[docs]class FluxPoints(object): """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) ) def _get_y_energy_unit(self, 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(ref_values.value.min()) - 1, np.log10(ref_values.value.max()) + 1, 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 in range(len(self.table)): y_ref = self.table["ref_" + self.sed_type].quantity[idx] norm = (y_values / y_ref).to_value("") norm_scan = self.table[idx]["norm_scan"] dloglike_scan = ( self.table[idx]["dloglike_scan"] - self.table[idx]["loglike"] ) z[idx] = _interp_likelihood_profile(norm_scan, dloglike_scan, 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 FluxPointEstimator(object): """Flux point estimator. Estimates flux points for a given spectrum observation dataset, energy groups 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 ---------- obs : `~gammapy.spectrum.SpectrumObservation` or `~gammapy.spectrum.SpectrumObservationList` Spectrum observation(s) groups : `~gammapy.spectrum.SpectrumEnergyGroups` Energy groups (usually output of `~gammapy.spectrum.SpectrumEnergyGroupMaker`) model : `~gammapy.spectrum.models.SpectralModel` Global model (usually output of `~gammapy.spectrum.SpectrumFit`) 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. """ def __init__( self, obs, groups, model, norm_min=0.2, norm_max=5, norm_n_values=11, norm_values=None, sigma=1, sigma_ul=2, ): if isinstance(obs, SpectrumObservation): obs = SpectrumObservationList([obs]) self.obs = SpectrumObservationList(obs) self.groups = groups self.model = ScaleModel(model) self.model.parameters["norm"].min = 0 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 @property def ref_model(self): return self.model.model def __str__(self): s = "{}:\n".format(self.__class__.__name__) s += str(self.obs) + "\n" s += str(self.groups) + "\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 group in self.groups: if group.bin_type != "normal": log.debug("Skipping energy group:\n{}".format(group)) continue row = self.estimate_flux_point(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")
[docs] def estimate_flux_point(self, e_group, steps="all"): """Estimate flux point for a single energy group. Parameters ---------- e_group : `SpectrumEnergyGroup` 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. """ # Put at log center of the bin e_min, e_max = e_group.energy_min, e_group.energy_max 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), ] ) quality_orig = self._set_quality(e_group) result.update(self.estimate_norm()) if steps == "all": steps = ["err", "errp-errn", "ul", "ts", "norm-scan"] if "err" in steps: result.update(self.estimate_norm_err()) 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(result)) self._restore_quality(quality_orig) 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="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.model.parameters.error("norm") return {"norm_err": norm_err}
[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.parameters["norm"].value result = self.fit.confidence(parameter="norm", sigma=self.sigma_ul) return {"norm_ul": result["errp"] + norm}
[docs] def estimate_norm_ts(self): """Estimate ts and sqrt(ts) for the flux point. Returns ------- result : dict Dict with ts and srtq_ts for the flux point. """ parameters = self.model.parameters loglike = self.fit.total_stat(parameters) norm_best_fit = parameters["norm"].value # store best fit amplitude, set amplitude of fit model to zero parameters["norm"].value = 0 loglike_null = self.fit.total_stat(parameters) parameters["norm"].value = 1.0 # compute sqrt TS ts = np.abs(loglike_null - loglike) sqrt_ts = np.sign(norm_best_fit) * np.sqrt(ts) return {"sqrt_ts": sqrt_ts, "ts": ts}
[docs] def estimate_norm_scan(self, flux_point): """Estimate likelihood profile for the norm parameter Returns ------- result : dict Dict with norm_scan and dloglike_scan for the flux point. """ # norm = self.model.parameters["norm"] result = self.fit.likelihood_profile("norm", values=self.norm_values) 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. """ from .fit import SpectrumFit self.fit = SpectrumFit(self.obs, self.model) result = self.fit.optimize() if result.success: norm = result.model.parameters["norm"].value self.model.parameters["norm"].value = norm else: emin, emax = self.fit.true_fit_range[0] log.warning( "Fit failed for flux point between {emin:.3f} and {emax:.3f}," " setting NaN.".format(emin=emin, emax=emax) ) norm = np.nan return {"norm": norm, "loglike": result.total_stat}
# TODO: clean up this helper function and maybe move it to SpectrumObservations def _set_quality(self, energy_group): quality_orig = [] for index in range(len(self.obs)): # Set quality bins to only bins in energy_group quality_orig_unit = self.obs[index].on_vector.quality quality_len = len(quality_orig_unit) quality_orig.append(quality_orig_unit) quality = np.zeros(quality_len, dtype=int) for bin in range(quality_len): if ( (bin < energy_group.bin_idx_min) or (bin > energy_group.bin_idx_max) or (energy_group.bin_type != "normal") ): quality[bin] = 1 self.obs[index].on_vector.quality = quality return quality_orig def _restore_quality(self, quality_orig): for index in range(len(quality_orig)): self.obs[index].on_vector.quality = quality_orig[index]
[docs]class FluxPointFit(Fit): """ Fit a set of flux points with a parametric model. Parameters ---------- model : `~gammapy.spectrum.models.SpectralModel` Spectral model data : `~gammapy.spectrum.FluxPoints` Flux points. Examples -------- Load flux points from file and fit with a power-law model:: from astropy import units as u from gammapy.spectrum import FluxPoints, FluxPointFit from gammapy.spectrum.models import PowerLaw filename = '$GAMMAPY_DATA/tests/spectrum/flux_points/diff_flux_points.fits' flux_points = FluxPoints.read(filename) model = PowerLaw() fit = FluxPointFit(model, flux_points) result = fit.run() print(result) print(result.model) """ def __init__(self, model, data, stat="chi2"): self._model = model self.data = data if stat in ["chi2", "chi2assym"]: self._stat = stat else: raise ValueError( "'{stat}' is not a valid fit statistic, please choose" " either 'chi2' or 'chi2assym'" ) @property def _stat_chi2(self): """Likelihood per bin given the current model parameters""" model = self._model(self.data.e_ref) data = self.data.table["dnde"].quantity sigma = self.data.table["dnde_err"].quantity return ((data - model) / sigma).to_value("") ** 2 @property def _stat_chi2_assym(self): """ Assymetric chi2 statistics for a list of flux points and model. """ model = self._model(self.data.e_ref) data = self.data.table["dnde"].quantity.to(model.unit) data_errp = self.data.table["dnde_errp"].quantity data_errn = self.data.table["dnde_errn"].quantity val_n = ((data - model) / data_errn).to_value("") ** 2 val_p = ((data - model) / data_errp).to_value("") ** 2 return np.where(model > data, val_p, val_n) @property def stat(self): if self._stat == "chi2": return self._stat_chi2 else: return self._stat_chi2_assym
[docs] def total_stat(self, parameters): """Total likelihood given the current model parameters""" return np.nansum(self.stat, dtype=np.float64)