Source code for gammapy.irf.energy_dispersion

# Licensed under a 3-clause BSD style license - see LICENSE.rst
from __future__ import absolute_import, division, print_function, unicode_literals
from collections import OrderedDict
import numpy as np
from scipy.special import erf
from astropy.io import fits
from astropy.coordinates import Angle
from astropy.units import Quantity
from astropy.table import Table
from ..utils.energy import EnergyBounds, Energy
from ..utils.scripts import make_path
from ..utils.nddata import NDDataArray, BinnedDataAxis
from ..utils.fits import energy_axis_to_ebounds

__all__ = ["EnergyDispersion", "EnergyDispersion2D"]


[docs]class EnergyDispersion(object): """Energy dispersion matrix. Data format specification: :ref:`gadf:ogip-rmf` Parameters ---------- e_true_lo, e_true_hi : `~astropy.units.Quantity` True energy axis binning e_reco_lo, e_reco_hi : `~astropy.units.Quantity` Reconstruced energy axis binning data : array_like 2-dim energy dispersion matrix Examples -------- Create a Gaussian energy dispersion matrix:: import numpy as np import astropy.units as u from gammapy.irf import EnergyDispersion energy = np.logspace(0, 1, 101) * u.TeV edisp = EnergyDispersion.from_gauss( e_true=energy, e_reco=energy, sigma=0.1, bias=0, ) Have a quick look: >>> print(edisp) >>> edisp.peek() See Also -------- EnergyDispersion2D """ default_interp_kwargs = dict(bounds_error=False, fill_value=0, method="nearest") """Default Interpolation kwargs for `~NDDataArray`. Fill zeros and do not interpolate""" def __init__( self, e_true_lo, e_true_hi, e_reco_lo, e_reco_hi, data, interp_kwargs=None, meta=None, ): if interp_kwargs is None: interp_kwargs = self.default_interp_kwargs axes = [ BinnedDataAxis( e_true_lo, e_true_hi, interpolation_mode="log", name="e_true" ), BinnedDataAxis( e_reco_lo, e_reco_hi, interpolation_mode="log", name="e_reco" ), ] self.data = NDDataArray(axes=axes, data=data, interp_kwargs=interp_kwargs) self.meta = OrderedDict(meta) if meta else OrderedDict() def __str__(self): ss = self.__class__.__name__ ss += "\n{}".format(self.data) return ss
[docs] def apply(self, data): """Apply energy dispersion. Computes the matrix product of ``data`` (which typically is model flux or counts in true energy bins) with the energy dispersion matrix. Parameters ---------- data : array_like 1-dim data array. Returns ------- convolved_data : array 1-dim data array after multiplication with the energy dispersion matrix """ if len(data) != self.e_true.nbins: raise ValueError( "Input size {} does not match true energy axis {}".format( len(data), self.e_true.nbins ) ) return np.dot(data, self.data.data)
@property def e_reco(self): """Reconstructed energy axis (`~gammapy.utils.nddata.BinnedDataAxis`)""" return self.data.axis("e_reco") @property def e_true(self): """True energy axis (`~gammapy.utils.nddata.BinnedDataAxis`)""" return self.data.axis("e_true") @property def pdf_matrix(self): """Energy dispersion PDF matrix (`~numpy.ndarray`). Rows (first index): True Energy Columns (second index): Reco Energy """ return self.data.data.value
[docs] def pdf_in_safe_range(self, lo_threshold, hi_threshold): """PDF matrix with bins outside threshold set to 0. Parameters ---------- lo_threshold : `~astropy.units.Quantity` Low reco energy threshold hi_threshold : `~astropy.units.Quantity` High reco energy threshold """ data = self.pdf_matrix.copy() idx = np.where( (self.e_reco.lo < lo_threshold) | (self.e_reco.hi > hi_threshold) ) data[:, idx] = 0 return data
[docs] @classmethod def from_gauss(cls, e_true, e_reco, sigma, bias, pdf_threshold=1e-6): """Create Gaussian energy dispersion matrix (`EnergyDispersion`). Calls :func:`gammapy.irf.EnergyDispersion2D.from_gauss` Parameters ---------- e_true : `~astropy.units.Quantity`, `~gammapy.utils.nddata.BinnedDataAxis` Bin edges of true energy axis e_reco : `~astropy.units.Quantity`, `~gammapy.utils.nddata.BinnedDataAxis` Bin edges of reconstructed energy axis bias : float or `~numpy.ndarray` Center of Gaussian energy dispersion, bias sigma : float or `~numpy.ndarray` RMS width of Gaussian energy dispersion, resolution pdf_threshold : float, optional Zero suppression threshold """ migra = np.linspace(1.0 / 3, 3, 200) # A dummy offset axis (need length 2 for interpolation to work) offset = Quantity([0, 1, 2], "deg") edisp = EnergyDispersion2D.from_gauss( e_true=e_true, migra=migra, sigma=sigma, bias=bias, offset=offset, pdf_threshold=pdf_threshold, ) return edisp.to_energy_dispersion(offset=offset[0], e_reco=e_reco)
[docs] @classmethod def from_diagonal_response(cls, e_true, e_reco=None): """Create energy dispersion from a diagonal response, i.e. perfect energy resolution This creates the matrix corresponding to a perfect energy response. It contains ones where the e_true center is inside the e_reco bin. It is a square diagonal matrix if e_true = e_reco. This is useful in cases where code always applies an edisp, but you don't want it to do anything. Parameters ---------- e_true, e_reco : `~astropy.units.Quantity` Energy bounds for true and reconstructed energy axis Examples -------- If ``e_true`` equals ``e_reco``, you get a diagonal matrix:: e_true = [0.5, 1, 2, 4, 6] * u.TeV edisp = EnergyDispersion.from_diagonal_response(e_true) edisp.plot_matrix() Example with different energy binnings:: e_true = [0.5, 1, 2, 4, 6] * u.TeV e_reco = [2, 4, 6] * u.TeV edisp = EnergyDispersion.from_diagonal_response(e_true, e_reco) edisp.plot_matrix() """ if e_reco is None: e_reco = e_true e_true_center = 0.5 * (e_true[1:] + e_true[:-1]) etrue_2d, ereco_lo_2d = np.meshgrid(e_true_center, e_reco[:-1]) etrue_2d, ereco_hi_2d = np.meshgrid(e_true_center, e_reco[1:]) data = np.logical_and(etrue_2d >= ereco_lo_2d, etrue_2d < ereco_hi_2d) data = np.transpose(data).astype("float") return cls( e_true_lo=e_true[:-1], e_true_hi=e_true[1:], e_reco_lo=e_reco[:-1], e_reco_hi=e_reco[1:], data=data, )
[docs] @classmethod def from_hdulist(cls, hdulist, hdu1="MATRIX", hdu2="EBOUNDS"): """Create `EnergyDispersion` object from `~astropy.io.fits.HDUList`. Parameters ---------- hdulist : `~astropy.io.fits.HDUList` HDU list with ``MATRIX`` and ``EBOUNDS`` extensions. hdu1 : str, optional HDU containing the energy dispersion matrix, default: MATRIX hdu2 : str, optional HDU containing the energy axis information, default, EBOUNDS """ matrix_hdu = hdulist[hdu1] ebounds_hdu = hdulist[hdu2] data = matrix_hdu.data header = matrix_hdu.header pdf_matrix = np.zeros([len(data), header["DETCHANS"]], dtype=np.float64) for i, l in enumerate(data): if l.field("N_GRP"): m_start = 0 for k in range(l.field("N_GRP")): pdf_matrix[ i, l.field("F_CHAN")[k] : l.field("F_CHAN")[k] + l.field("N_CHAN")[k], ] = l.field("MATRIX")[m_start : m_start + l.field("N_CHAN")[k]] m_start += l.field("N_CHAN")[k] e_reco = EnergyBounds.from_ebounds(ebounds_hdu) e_true = EnergyBounds.from_rmf_matrix(matrix_hdu) return cls( e_true_lo=e_true.lower_bounds, e_true_hi=e_true.upper_bounds, e_reco_lo=e_reco.lower_bounds, e_reco_hi=e_reco.upper_bounds, data=pdf_matrix, )
[docs] @classmethod def read(cls, filename, hdu1="MATRIX", hdu2="EBOUNDS"): """Read from file. Parameters ---------- filename : `~gammapy.extern.pathlib.Path`, str File to read hdu1 : str, optional HDU containing the energy dispersion matrix, default: MATRIX hdu2 : str, optional HDU containing the energy axis information, default, EBOUNDS """ filename = make_path(filename) with fits.open(str(filename), memmap=False) as hdulist: edisp = cls.from_hdulist(hdulist, hdu1=hdu1, hdu2=hdu2) return edisp
[docs] def to_hdulist(self, **kwargs): """Convert RMF to FITS HDU list format. Parameters ---------- header : `~astropy.io.fits.Header` Header to be written in the fits file. energy_unit : str Unit in which the energy is written in the HDU list Returns ------- hdulist : `~astropy.io.fits.HDUList` RMF in HDU list format. Notes ----- For more info on the RMF FITS file format see: https://heasarc.gsfc.nasa.gov/docs/heasarc/caldb/docs/summary/cal_gen_92_002_summary.html """ # Cannot use table_to_fits here due to variable length array # http://docs.astropy.org/en/v1.0.4/io/fits/usage/unfamiliar.html table = self.to_table() name = table.meta.pop("name") header = fits.Header() header.update(table.meta) cols = table.columns c0 = fits.Column( name=cols[0].name, format="E", array=cols[0], unit="{}".format(cols[0].unit) ) c1 = fits.Column( name=cols[1].name, format="E", array=cols[1], unit="{}".format(cols[1].unit) ) c2 = fits.Column(name=cols[2].name, format="I", array=cols[2]) c3 = fits.Column(name=cols[3].name, format="PI()", array=cols[3]) c4 = fits.Column(name=cols[4].name, format="PI()", array=cols[4]) c5 = fits.Column(name=cols[5].name, format="PE()", array=cols[5]) hdu = fits.BinTableHDU.from_columns( [c0, c1, c2, c3, c4, c5], header=header, name=name ) ebounds = energy_axis_to_ebounds(self.e_reco.bins) prim_hdu = fits.PrimaryHDU() return fits.HDUList([prim_hdu, hdu, ebounds])
[docs] def to_table(self): """Convert to `~astropy.table.Table`. The output table is in the OGIP RMF format. https://heasarc.gsfc.nasa.gov/docs/heasarc/caldb/docs/memos/cal_gen_92_002/cal_gen_92_002.html#Tab:1 """ rows = self.pdf_matrix.shape[0] n_grp = [] f_chan = np.ndarray(dtype=np.object, shape=rows) n_chan = np.ndarray(dtype=np.object, shape=rows) matrix = np.ndarray(dtype=np.object, shape=rows) # Make RMF type matrix for i, row in enumerate(self.data.data.value): pos = np.nonzero(row)[0] borders = np.where(np.diff(pos) != 1)[0] # add 1 to borders for correct behaviour of np.split groups = np.asarray(np.split(pos, borders + 1)) n_grp_temp = groups.shape[0] if groups.size > 0 else 1 n_chan_temp = np.asarray([val.size for val in groups]) try: f_chan_temp = np.asarray([val[0] for val in groups]) except IndexError: f_chan_temp = np.zeros(1) n_grp.append(n_grp_temp) f_chan[i] = f_chan_temp n_chan[i] = n_chan_temp matrix[i] = row[pos] n_grp = np.asarray(n_grp, dtype=np.int16) # Get total number of groups and channel subsets numgrp, numelt = 0, 0 for val, val2 in zip(n_grp, n_chan): numgrp += np.sum(val) numelt += np.sum(val2) table = Table() table["ENERG_LO"] = self.e_true.lo table["ENERG_HI"] = self.e_true.hi table["N_GRP"] = n_grp table["F_CHAN"] = f_chan table["N_CHAN"] = n_chan table["MATRIX"] = matrix table.meta = OrderedDict( [ ("name", "MATRIX"), ("chantype", "PHA"), ("hduclass", "OGIP"), ("hduclas1", "RESPONSE"), ("hduclas2", "RSP_MATRIX"), ("detchans", self.e_reco.nbins), ("numgrp", numgrp), ("numelt", numelt), ("tlmin4", 0), ] ) return table
[docs] def write(self, filename, **kwargs): """Write to file.""" filename = make_path(filename) self.to_hdulist().writeto(str(filename), **kwargs)
[docs] def get_resolution(self, e_true): """Get energy resolution for a given true energy. The resolution is given as a percentage of the true energy Parameters ---------- e_true : `~astropy.units.Quantity` True energy """ var = self._get_variance(e_true) idx_true = self.e_true.find_node(e_true) e_true_real = self.e_true.nodes[idx_true] return np.sqrt(var) / e_true_real
[docs] def get_bias(self, e_true): r"""Get reconstruction bias for a given true energy. Bias is defined as .. math:: \frac{E_{reco}-E_{true}}{E_{true}} Parameters ---------- e_true : `~astropy.units.Quantity` True energy """ e_reco = self.get_mean(e_true) idx_true = self.e_true.find_node(e_true) e_true_real = self.e_true.nodes[idx_true] bias = (e_reco - e_true_real) / e_true_real return bias
[docs] def get_mean(self, e_true): """Get mean reconstructed energy for a given true energy.""" # find pdf for true energies idx = self.e_true.find_node(e_true) pdf = self.data.data[idx] # compute sum along reconstructed energy # axis to determine the mean norm = np.sum(pdf, axis=-1) temp = np.sum(pdf * self.e_reco.nodes, axis=-1) return temp / norm
def _get_variance(self, e_true): """Get variance of log reconstructed energy.""" # evaluate the pdf at given true energies idx = self.e_true.find_node(e_true) pdf = self.data.data[idx] # compute mean mean = self.get_mean(e_true) # create array of reconstructed-energy nodes # for each given true energy value # (first axis is reconstructed energy) erec = self.e_reco.nodes erec = np.repeat(erec, max(np.sum(mean.shape), 1)).reshape( erec.shape + mean.shape ) # compute deviation from mean # (and move reconstructed energy axis to last axis) temp_ = (erec - mean) ** 2 temp = np.rollaxis(temp_, 1) # compute sum along reconstructed energy # axis to determine the variance norm = np.sum(pdf, axis=-1) var = np.sum(temp * pdf, axis=-1) return var / norm
[docs] def to_sherpa(self, name): """Convert to `sherpa.astro.data.DataRMF`. Parameters ---------- name : str Instance name """ from sherpa.astro.data import DataRMF from sherpa.utils import SherpaUInt, SherpaFloat # Need to modify RMF data # see https://github.com/sherpa/sherpa/blob/master/sherpa/astro/io/pyfits_backend.py#L727 table = self.to_table() n_grp = table["N_GRP"].data.astype(SherpaUInt) f_chan = table["F_CHAN"].data n_chan = table["N_CHAN"].data matrix = table["MATRIX"].data good = n_grp > 0 matrix = matrix[good] matrix = np.concatenate([row for row in matrix]) matrix = matrix.astype(SherpaFloat) good = n_grp > 0 f_chan = f_chan[good] f_chan = np.concatenate([row for row in f_chan]).astype(SherpaUInt) n_chan = n_chan[good] n_chan = np.concatenate([row for row in n_chan]).astype(SherpaUInt) return DataRMF( name=name, energ_lo=table["ENERG_LO"].quantity.to_value("keV").astype(SherpaFloat), energ_hi=table["ENERG_HI"].quantity.to_value("keV").astype(SherpaFloat), matrix=matrix, n_grp=n_grp, n_chan=n_chan, f_chan=f_chan, detchans=self.e_reco.nbins, e_min=self.e_reco.lo.to_value("keV"), e_max=self.e_reco.hi.to_value("keV"), offset=0, )
[docs] def plot_matrix(self, ax=None, show_energy=None, add_cbar=False, **kwargs): """Plot PDF matrix. Parameters ---------- ax : `~matplotlib.axes.Axes`, optional Axis show_energy : `~astropy.units.Quantity`, optional Show energy, e.g. threshold, as vertical line add_cbar : bool Add a colorbar to the plot. Returns ------- ax : `~matplotlib.axes.Axes` Axis """ import matplotlib.pyplot as plt from matplotlib.colors import PowerNorm kwargs.setdefault("cmap", "GnBu") norm = PowerNorm(gamma=0.5) kwargs.setdefault("norm", norm) ax = plt.gca() if ax is None else ax e_true = self.e_true.bins e_reco = self.e_reco.bins x = e_true.value y = e_reco.value z = self.pdf_matrix caxes = ax.pcolormesh(x, y, z.T, **kwargs) if show_energy is not None: ener_val = show_energy.to_value(self.reco_energy.unit) ax.hlines(ener_val, 0, 200200, linestyles="dashed") if add_cbar: label = "Probability density (A.U.)" cbar = ax.figure.colorbar(caxes, ax=ax, label=label) ax.set_xlabel(r"$E_\mathrm{{True}}$ [{unit}]".format(unit=e_true.unit)) ax.set_ylabel(r"$E_\mathrm{{Reco}}$ [{unit}]".format(unit=e_reco.unit)) ax.set_xscale("log") ax.set_yscale("log") ax.set_xlim(x.min(), x.max()) ax.set_ylim(y.min(), y.max()) return ax
[docs] def plot_bias(self, ax=None, **kwargs): """Plot reconstruction bias. See `~gammapy.irf.EnergyDispersion.get_bias` method. Parameters ---------- ax : `~matplotlib.axes.Axes`, optional Axis """ import matplotlib.pyplot as plt ax = plt.gca() if ax is None else ax x = self.e_true.nodes.to_value("TeV") y = self.get_bias(self.e_true.nodes) ax.plot(x, y, **kwargs) ax.set_xlabel(r"$E_\mathrm{{True}}$ [TeV]") ax.set_ylabel(r"($E_\mathrm{{True}} - E_\mathrm{{Reco}} / E_\mathrm{{True}}$)") ax.set_xscale("log") return ax
[docs] def peek(self, figsize=(15, 5)): """Quick-look summary plot.""" import matplotlib.pyplot as plt fig, axes = plt.subplots(nrows=1, ncols=2, figsize=figsize) self.plot_bias(ax=axes[0]) self.plot_matrix(ax=axes[1]) plt.tight_layout()
[docs]class EnergyDispersion2D(object): """Offset-dependent energy dispersion matrix. Data format specification: :ref:`gadf:edisp_2d` Parameters ---------- e_true_lo, e_true_hi : `~astropy.units.Quantity` True energy axis binning migra_lo, migra_hi : `~numpy.ndarray` Energy migration axis binning offset_lo, offset_hi : `~astropy.coordinates.Angle` Field of view offset axis binning data : `~numpy.ndarray` Energy dispersion probability density Examples -------- Read energy dispersion IRF from disk: >>> from gammapy.irf import EnergyDispersion2D >>> from gammapy.utils.energy import EnergyBounds >>> filename = '$GAMMAPY_DATA/tests/irf/hess/pa/hess_edisp_2d_023523.fits.gz' >>> edisp2d = EnergyDispersion2D.read(filename, hdu='ENERGY DISPERSION') >>> print(edisp2d) EnergyDispersion2D NDDataArray summary info e_true : size = 15, min = 0.125 TeV, max = 80.000 TeV migra : size = 100, min = 0.051, max = 10.051 offset : size = 6, min = 0.125 deg, max = 2.500 deg Data : size = 9000, min = 0.000, max = 3.405 Create energy dispersion matrix (`~gammapy.irf.EnergyDispersion`) for a given field of view offset and energy binning: >>> energy = EnergyBounds.equal_log_spacing(0.1,20,60, 'TeV') >>> edisp = edisp2d.to_energy_dispersion(offset='1.2 deg', e_reco=energy, e_true=energy) >>> print(edisp) EnergyDispersion NDDataArray summary info e_true : size = 60, min = 0.105 TeV, max = 19.136 TeV e_reco : size = 60, min = 0.105 TeV, max = 19.136 TeV Data : size = 3600, min = 0.000, max = 0.266 See Also -------- EnergyDispersion """ default_interp_kwargs = dict(bounds_error=False, fill_value=None) """Default Interpolation kwargs for `~gammapy.utils.nddata.NDDataArray`. Extrapolate.""" def __init__( self, e_true_lo, e_true_hi, migra_lo, migra_hi, offset_lo, offset_hi, data, interp_kwargs=None, meta=None, ): if interp_kwargs is None: interp_kwargs = self.default_interp_kwargs axes = [ BinnedDataAxis( e_true_lo, e_true_hi, interpolation_mode="log", name="e_true" ), BinnedDataAxis( migra_lo, migra_hi, interpolation_mode="linear", name="migra" ), BinnedDataAxis( offset_lo, offset_hi, interpolation_mode="linear", name="offset" ), ] self.data = NDDataArray(axes=axes, data=data, interp_kwargs=interp_kwargs) self.meta = OrderedDict(meta) if meta else OrderedDict() def __str__(self): ss = self.__class__.__name__ ss += "\n{}".format(self.data) return ss
[docs] @classmethod def from_gauss(cls, e_true, migra, bias, sigma, offset, pdf_threshold=1e-6): """Create Gaussian energy dispersion matrix (`EnergyDispersion2D`). The output matrix will be Gaussian in (e_true / e_reco). The ``bias`` and ``sigma`` should be either floats or arrays of same dimension than ``e_true``. ``bias`` refers to the mean value of the ``migra`` distribution minus one, i.e. ``bias=0`` means no bias. Note that, the output matrix is flat in offset. Parameters ---------- e_true : `~astropy.units.Quantity`, `~gammapy.utils.nddata.BinnedDataAxis` Bin edges of true energy axis migra : `~astropy.units.Quantity`, `~gammapy.utils.nddata.BinnedDataAxis` Bin edges of migra axis bias : float or `~numpy.ndarray` Center of Gaussian energy dispersion, bias sigma : float or `~numpy.ndarray` RMS width of Gaussian energy dispersion, resolution offset : `~astropy.units.Quantity`, `~gammapy.utils.nddata.BinnedDataAxis` Bin edges of offset pdf_threshold : float, optional Zero suppression threshold """ e_true = EnergyBounds(e_true) # erf does not work with Quantities true = e_true.log_centers.to_value("TeV") true2d, migra2d = np.meshgrid(true, migra) migra2d_lo = migra2d[:-1, :] migra2d_hi = migra2d[1:, :] # Analytical formula for integral of Gaussian s = np.sqrt(2) * sigma t1 = (migra2d_hi - 1 - bias) / s t2 = (migra2d_lo - 1 - bias) / s pdf = (erf(t1) - erf(t2)) / 2 pdf_array = pdf.T[:, :, np.newaxis] * np.ones(len(offset) - 1) pdf_array = np.where(pdf_array > pdf_threshold, pdf_array, 0) return cls( e_true[:-1], e_true[1:], migra[:-1], migra[1:], offset[:-1], offset[1:], pdf_array, )
[docs] @classmethod def from_table(cls, table): """Create from `~astropy.table.Table`.""" if "ENERG_LO" in table.colnames: e_lo = table["ENERG_LO"].quantity[0] e_hi = table["ENERG_HI"].quantity[0] elif "ETRUE_LO" in table.colnames: e_lo = table["ETRUE_LO"].quantity[0] e_hi = table["ETRUE_HI"].quantity[0] else: raise ValueError( 'Invalid column names. Need "ENERG_LO/ENERG_HI" or "ETRUE_LO/ETRUE_HI"' ) o_lo = table["THETA_LO"].quantity[0] o_hi = table["THETA_HI"].quantity[0] m_lo = table["MIGRA_LO"].quantity[0] m_hi = table["MIGRA_HI"].quantity[0] # TODO Why does this need to be transposed? matrix = table["MATRIX"].quantity[0].transpose() return cls( e_true_lo=e_lo, e_true_hi=e_hi, offset_lo=o_lo, offset_hi=o_hi, migra_lo=m_lo, migra_hi=m_hi, data=matrix, )
[docs] @classmethod def from_hdulist(cls, hdulist, hdu="edisp_2d"): """Create from `~astropy.io.fits.HDUList`.""" return cls.from_table(Table.read(hdulist[hdu]))
[docs] @classmethod def read(cls, filename, hdu="edisp_2d"): """Read from FITS file. Parameters ---------- filename : str File name """ filename = make_path(filename) with fits.open(str(filename), memmap=False) as hdulist: edisp = cls.from_hdulist(hdulist, hdu) return edisp
[docs] def to_energy_dispersion(self, offset, e_true=None, e_reco=None): """Detector response R(Delta E_reco, Delta E_true) Probability to reconstruct an energy in a given true energy band in a given reconstructed energy band Parameters ---------- offset : `~astropy.coordinates.Angle` Offset e_true : `~gammapy.utils.energy.EnergyBounds`, None True energy axis e_reco : `~gammapy.utils.energy.EnergyBounds` Reconstructed energy axis Returns ------- edisp : `~gammapy.irf.EnergyDispersion` Energy dispersion matrix """ offset = Angle(offset) e_true = self.data.axis("e_true").bins if e_true is None else e_true e_reco = self.data.axis("e_true").bins if e_reco is None else e_reco e_true = EnergyBounds(e_true) e_reco = EnergyBounds(e_reco) data = [] for energy in e_true.log_centers: vec = self.get_response(offset=offset, e_true=energy, e_reco=e_reco) data.append(vec) data = np.asarray(data) e_lo, e_hi = e_true[:-1], e_true[1:] ereco_lo, ereco_hi = (e_reco[:-1], e_reco[1:]) return EnergyDispersion( e_true_lo=e_lo, e_true_hi=e_hi, e_reco_lo=ereco_lo, e_reco_hi=ereco_hi, data=data, )
[docs] def get_response(self, offset, e_true, e_reco=None, migra_step=5e-3): """Detector response R(Delta E_reco, E_true) Probability to reconstruct a given true energy in a given reconstructed energy band. In each reco bin, you integrate with a riemann sum over the default migra bin of your analysis. Parameters ---------- e_true : `~gammapy.utils.energy.Energy` True energy e_reco : `~gammapy.utils.energy.EnergyBounds`, None Reconstructed energy axis offset : `~astropy.coordinates.Angle` Offset migra_step : float Integration step in migration Returns ------- rv : `~numpy.ndarray` Redistribution vector """ e_true = Energy(e_true) if e_reco is None: # Default: e_reco nodes = migra nodes * e_true nodes migra_axis = self.data.axis("migra") e_reco = EnergyBounds.from_lower_and_upper_bounds( migra_axis.lo * e_true, migra_axis.hi * e_true ) else: # Translate given e_reco binning to migra at bin center e_reco = EnergyBounds(e_reco) # migration value of e_reco bounds migra_e_reco = e_reco / e_true # Define a vector of migration with mig_step step mrec_min = self.data.axis("migra").lo[0] mrec_max = self.data.axis("migra").hi[-1] mig_array = np.arange(mrec_min, mrec_max, migra_step) # Compute energy dispersion probability dP/dm for each element of migration array vals = self.data.evaluate(offset=offset, e_true=e_true, migra=mig_array) # Compute normalized cumulative sum to prepare integration with np.errstate(invalid="ignore"): tmp = np.nan_to_num(np.cumsum(vals) / np.sum(vals)) # Determine positions (bin indices) of e_reco bounds in migration array pos_mig = np.digitize(migra_e_reco, mig_array) - 1 # We ensure that no negative values are found pos_mig = np.maximum(pos_mig, 0) # We compute the difference between 2 successive bounds in e_reco # to get integral over reco energy bin integral = np.diff(tmp[pos_mig]) return integral
[docs] def plot_migration(self, ax=None, offset=None, e_true=None, migra=None, **kwargs): """Plot energy dispersion for given offset and true energy. Parameters ---------- ax : `~matplotlib.axes.Axes`, optional Axis offset : `~astropy.coordinates.Angle`, optional Offset e_true : `~gammapy.utils.energy.Energy`, optional True energy migra : `~numpy.array`, list, optional Migration nodes Returns ------- ax : `~matplotlib.axes.Axes` Axis """ import matplotlib.pyplot as plt ax = plt.gca() if ax is None else ax if offset is None: offset = Angle([1], "deg") else: offset = np.atleast_1d(Angle(offset)) if e_true is None: e_true = Energy([0.1, 1, 10], "TeV") else: e_true = np.atleast_1d(Energy(e_true)) migra = self.data.axis("migra").nodes if migra is None else migra for ener in e_true: for off in offset: disp = self.data.evaluate(offset=off, e_true=ener, migra=migra) label = "offset = {0:.1f}\nenergy = {1:.1f}".format(off, ener) ax.plot(migra, disp, label=label, **kwargs) ax.set_xlabel(r"$E_\mathrm{{Reco}} / E_\mathrm{{True}}$") ax.set_ylabel("Probability density") ax.legend(loc="upper left") return ax
[docs] def plot_bias(self, ax=None, offset=None, add_cbar=False, **kwargs): """Plot migration as a function of true energy for a given offset. Parameters ---------- ax : `~matplotlib.axes.Axes`, optional Axis offset : `~astropy.coordinates.Angle`, optional Offset add_cbar : bool Add a colorbar to the plot. kwargs : dict Keyword arguments passed to `~matplotlib.pyplot.pcolormesh`. Returns ------- ax : `~matplotlib.axes.Axes` Axis """ from matplotlib.colors import PowerNorm import matplotlib.pyplot as plt kwargs.setdefault("cmap", "GnBu") kwargs.setdefault("norm", PowerNorm(gamma=0.5)) ax = plt.gca() if ax is None else ax if offset is None: offset = Angle(1, "deg") e_true = self.data.axis("e_true").bins migra = self.data.axis("migra").bins x = e_true.value y = migra.value z = self.data.evaluate( offset=offset, e_true=e_true.reshape(1, -1, 1), migra=migra.reshape(1, 1, -1), ).value[0] caxes = ax.pcolormesh(x, y, z.T, **kwargs) if add_cbar: label = "Probability density (A.U.)" ax.figure.colorbar(caxes, ax=ax, label=label) ax.set_xlabel(r"$E_\mathrm{{True}}$ [{unit}]".format(unit=e_true.unit)) ax.set_ylabel(r"$E_\mathrm{{Reco}} / E_\mathrm{{True}}$") ax.set_xlim(x.min(), x.max()) ax.set_ylim(y.min(), y.max()) ax.set_xscale("log") return ax
[docs] def peek(self, figsize=(15, 5)): """Quick-look summary plots. Parameters ---------- figsize : (float, float) Size of the resulting plot """ import matplotlib.pyplot as plt fig, axes = plt.subplots(nrows=1, ncols=3, figsize=figsize) self.plot_bias(ax=axes[0]) self.plot_migration(ax=axes[1]) edisp = self.to_energy_dispersion(offset="1 deg") edisp.plot_matrix(ax=axes[2]) plt.tight_layout()
[docs] def to_table(self): """Convert to `~astropy.table.Table`.""" meta = self.meta.copy() table = Table(meta=meta) table["ENERG_LO"] = self.data.axis("e_true").lo[np.newaxis] table["ENERG_HI"] = self.data.axis("e_true").hi[np.newaxis] table["MIGRA_LO"] = self.data.axis("migra").hi[np.newaxis] table["MIGRA_HI"] = self.data.axis("migra").hi[np.newaxis] table["THETA_LO"] = self.data.axis("offset").lo[np.newaxis] table["THETA_HI"] = self.data.axis("offset").hi[np.newaxis] table["MATRIX"] = self.data.data.T[np.newaxis] return table
[docs] def to_fits(self, name="ENERGY DISPERSION"): """Convert to `~astropy.io.fits.BinTable`.""" return fits.BinTableHDU(self.to_table(), name=name)