def generate_energies(self, t_exp, area, prng=None, quiet=False):
"""
Generate photon energies from this spectrum
given an exposure time and effective area.
Parameters
----------
t_exp : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The exposure time in seconds.
area : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The effective area in cm**2. If one is creating
events for a SIMPUT file, a constant should be
used and it must be large enough so that a
sufficiently large sample is drawn for the ARF.
prng : :class:`~numpy.random.RandomState` object, integer, or None
A pseudo-random number generator. Typically will only
be specified if you have a reason to generate the same
set of random numbers, such as for a test. Default is None,
which sets the seed based on the system time.
quiet : boolean, optional
If True, log messages will not be displayed when
creating energies. Useful if you have to loop over
a lot of spectra. Default: False
"""
t_exp = parse_value(t_exp, "s")
area = parse_value(area, "cm**2")
prng = parse_prng(prng)
rate = area*self.total_flux.value
energy = _generate_energies(self, t_exp, rate, prng, quiet=quiet)
flux = np.sum(energy)*erg_per_keV/t_exp/area
energies = Energies(energy, flux)
return energies
def generate_energies(self, t_exp, area, prng=None, quiet=False):
"""
Generate photon energies from this spectrum
given an exposure time and effective area.
Parameters
----------
t_exp : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The exposure time in seconds.
area : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The effective area in cm**2. If one is creating
events for a SIMPUT file, a constant should be
used and it must be large enough so that a
sufficiently large sample is drawn for the ARF.
prng : :class:`~numpy.random.RandomState` object, integer, or None
A pseudo-random number generator. Typically will only
be specified if you have a reason to generate the same
set of random numbers, such as for a test. Default is None,
which sets the seed based on the system time.
quiet : boolean, optional
If True, log messages will not be displayed when
creating energies. Useful if you have to loop over
a lot of spectra. Default: False
"""
t_exp = parse_value(t_exp, "s")
area = parse_value(area, "cm**2")
prng = parse_prng(prng)
rate = area*self.total_flux.value
energy = _generate_energies(self, t_exp, rate, prng, quiet=quiet)
flux = np.sum(energy)*erg_per_keV/t_exp/area
energies = Energies(energy, flux)
return energies
def _from_xspec(cls, xspec_in, emin, emax, nbins):
emin = parse_value(emin, "keV")
emax = parse_value(emax, "keV")
tmpdir = tempfile.mkdtemp()
curdir = os.getcwd()
os.chdir(tmpdir)
xspec_in.append("dummyrsp %g %g %d lin\n" % (emin, emax, nbins))
xspec_in += ["set fp [open spec_therm.xspec w+]\n",
"tclout energies\n", "puts $fp $xspec_tclout\n",
"tclout modval\n", "puts $fp $xspec_tclout\n",
"close $fp\n", "quit\n"]
f_xin = open("xspec.in", "w")
f_xin.writelines(xspec_in)
f_xin.close()
logfile = os.path.join(curdir, "xspec.log")
with open(logfile, "ab") as xsout:
subprocess.call(["xspec", "-", "xspec.in"],
stdout=xsout, stderr=xsout)
f_s = open("spec_therm.xspec", "r")
lines = f_s.readlines()
f_s.close()
ebins = np.array(lines[0].split()).astype("float64")
de = np.diff(ebins)[0]
flux = np.array(lines[1].split()).astype("float64")/de
os.chdir(curdir)
shutil.rmtree(tmpdir)
return cls(ebins, flux)
def rescale_flux(self, new_flux, emin=None, emax=None, flux_type="photons"):
"""
Rescale the flux of the spectrum, optionally using
a specific energy band.
Parameters
----------
new_flux : float
The new flux in units of photons/s/cm**2.
emin : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`, optional
The minimum energy of the band to consider,
in keV. Default: Use the minimum energy of
the entire spectrum.
emax : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`, optional
The maximum energy of the band to consider,
in keV. Default: Use the maximum energy of
the entire spectrum.
flux_type : string, optional
The units of the flux to use in the rescaling:
"photons": photons/s/cm**2
"energy": erg/s/cm**2
"""
if emin is None:
emin = self.ebins[0].value
if emax is None:
emax = self.ebins[-1].value
emin = parse_value(emin, "keV")
emax = parse_value(emax, 'keV')
idxs = np.logical_and(self.emid.value >= emin, self.emid.value <= emax)
if flux_type == "photons":
f = self.flux[idxs].sum()*self.de
elif flux_type == "energy":
f = (self.flux*self.emid.to("erg"))[idxs].sum()*self.de
self.flux *= new_flux/f.value
self._compute_total_flux()
def from_models(cls, name, spectral_model, spatial_model,
t_exp, area, prng=None):
"""
Generate a single photon list from a spectral and a spatial
model.
Parameters
----------
name : string
The name of the photon list. This will also be the prefix
of any photon list file that is written from this photon list.
spectral_model : :class:`~soxs.spectra.Spectrum`
The spectral model to use to generate the event energies.
spatial_model : :class:`~soxs.spatial.SpatialModel`
The spatial model to use to generate the event coordinates.
t_exp : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The exposure time in seconds.
area : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The effective area in cm**2. If one is creating
events for a SIMPUT file, a constant should be
used and it must be large enough so that a
sufficiently large sample is drawn for the ARF.
prng : :class:`~numpy.random.RandomState` object, integer, or None
A pseudo-random number generator. Typically will only
be specified if you have a reason to generate the same
set of random numbers, such as for a test. Default is None,
which sets the seed based on the system time.
"""
prng = parse_prng(prng)
t_exp = parse_value(t_exp, "s")
area = parse_value(area, "cm**2")
e = spectral_model.generate_energies(t_exp, area, prng=prng)
ra, dec = spatial_model.generate_coords(e.size, prng=prng)
return cls(name, ra, dec, e, e.flux)
def add_emission_line(self, line_center, line_width, line_amp,
line_type="gaussian"):
"""
Add an emission line to this spectrum.
Parameters
----------
line_center : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The line center position in units of keV, in the observer frame.
line_width : one or more float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The line width (FWHM) in units of keV, in the observer frame. Can also
input the line width in units of velocity in the rest frame. For the Voigt
profile, a list, tuple, or array of two values should be provided since there
are two line widths, the Lorentzian and the Gaussian (in that order).
line_amp : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The integrated line amplitude in the units of the flux
line_type : string, optional
The line profile type. Default: "gaussian"
"""
line_center = parse_value(line_center, "keV")
line_width = parse_value(line_width, "keV", equivalence=line_width_equiv(line_center))
line_amp = parse_value(line_amp, self._units)
if line_type == "gaussian":
sigma = line_width / sigma_to_fwhm
line_amp /= sqrt2pi * sigma
f = Gaussian1D(line_amp, line_center, sigma)
else:
raise NotImplementedError("Line profile type '%s' " % line_type +
"not implemented!")
self.flux += u.Quantity(f(self.emid.value), self._units)
self._compute_total_flux()
def add_absorption_line(self, line_center, line_width, equiv_width,
line_type='gaussian'):
"""
Add an absorption line to this spectrum.
Parameters
----------
line_center : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The line center position in units of keV, in the observer frame.
line_width : one or more float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The line width (FWHM) in units of keV, in the observer frame. Can also
input the line width in units of velocity in the rest frame. For the Voigt
profile, a list, tuple, or array of two values should be provided since there
are two line widths, the Lorentzian and the Gaussian (in that order).
equiv_width : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The equivalent width of the line, in units of milli-Angstrom
line_type : string, optional
The line profile type. Default: "gaussian"
"""
line_center = parse_value(line_center, "keV")
line_width = parse_value(line_width, "keV", equivalence=line_width_equiv(line_center))
equiv_width = parse_value(equiv_width, "1.0e-3*angstrom") # in milliangstroms
equiv_width *= 1.0e-3 # convert to angstroms
if line_type == "gaussian":
sigma = line_width / sigma_to_fwhm
B = equiv_width*line_center*line_center
B /= hc * sqrt2pi * sigma
f = Gaussian1D(B, line_center, sigma)
else:
raise NotImplementedError("Line profile type '%s' " % line_type +
"not implemented!")
self.flux *= np.exp(-f(self.emid.value))
self._compute_total_flux()
def rescale_flux(self, new_flux, emin=None, emax=None, flux_type="photons"):
"""
Rescale the flux of the spectrum, optionally using
a specific energy band.
Parameters
----------
new_flux : float
The new flux in units of photons/s/cm**2.
emin : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`, optional
The minimum energy of the band to consider,
in keV. Default: Use the minimum energy of
the entire spectrum.
emax : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`, optional
The maximum energy of the band to consider,
in keV. Default: Use the maximum energy of
the entire spectrum.
flux_type : string, optional
The units of the flux to use in the rescaling:
"photons": photons/s/cm**2
"energy": erg/s/cm**2
"""
if emin is None:
emin = self.ebins[0].value
if emax is None:
emax = self.ebins[-1].value
emin = parse_value(emin, "keV")
emax = parse_value(emax, 'keV')
idxs = np.logical_and(self.emid.value >= emin, self.emid.value <= emax)
if flux_type == "photons":
f = self.flux[idxs].sum()*self.de
elif flux_type == "energy":
f = (self.flux*self.emid.to("erg"))[idxs].sum()*self.de
self.flux *= new_flux/f.value
self._compute_total_flux()
def add_absorption_line(self, line_center, line_width, equiv_width,
line_type='gaussian'):
"""
Add an absorption line to this spectrum.
Parameters
----------
line_center : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The line center position in units of keV, in the observer frame.
line_width : one or more float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The line width (FWHM) in units of keV, in the observer frame. Can also
input the line width in units of velocity in the rest frame. For the Voigt
profile, a list, tuple, or array of two values should be provided since there
are two line widths, the Lorentzian and the Gaussian (in that order).
equiv_width : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The equivalent width of the line, in units of milli-Angstrom
line_type : string, optional
The line profile type. Default: "gaussian"
"""
line_center = parse_value(line_center, "keV")
line_width = parse_value(line_width, "keV", equivalence=line_width_equiv(line_center))
equiv_width = parse_value(equiv_width, "1.0e-3*angstrom") # in milliangstroms
equiv_width *= 1.0e-3 # convert to angstroms
if line_type == "gaussian":
sigma = line_width / sigma_to_fwhm
B = equiv_width*line_center*line_center
B /= hc * sqrt2pi * sigma
f = Gaussian1D(B, line_center, sigma)
else:
raise NotImplementedError("Line profile type '%s' " % line_type +
"not implemented!")
self.flux *= np.exp(-f(self.emid.value))
self._compute_total_flux()
def generate_fluxes(exp_time, area, fov, prng):
from soxs.data import cdf_fluxes, cdf_gal, cdf_agn
exp_time = parse_value(exp_time, "s")
area = parse_value(area, "cm**2")
fov = parse_value(fov, "arcmin")
logf = np.log10(cdf_fluxes)
n_gal = np.rint(cdf_gal[-1])
n_agn = np.rint(cdf_agn[-1])
F_gal = cdf_gal / cdf_gal[-1]
F_agn = cdf_agn / cdf_agn[-1]
f_gal = InterpolatedUnivariateSpline(F_gal, logf)
f_agn = InterpolatedUnivariateSpline(F_agn, logf)
eph_mean_erg = 1.0*erg_per_keV
S_min_obs = eph_mean_erg/(exp_time*area)
mylog.debug("Flux of %g erg/cm^2/s gives roughly "
"one photon during exposure." % S_min_obs)
fov_area = fov**2
n_gal = int(n_gal*fov_area/3600.0)
n_agn = int(n_agn*fov_area/3600.0)
mylog.debug("%d AGN, %d galaxies in the FOV." % (n_agn, n_gal))
randvec1 = prng.uniform(size=n_agn)
agn_fluxes = 10**f_agn(randvec1)
randvec2 = prng.uniform(size=n_gal)
gal_fluxes = 10**f_gal(randvec2)
return agn_fluxes, gal_fluxes
def generate_energies(self, t_exp, fov, prng=None,
quiet=False):
"""
Generate photon energies from this convolved
background spectrum given an exposure time and
field of view.
Parameters
----------
t_exp : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The exposure time in seconds.
fov : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The width of the field of view on a side
in arcminutes.
prng : :class:`~numpy.random.RandomState` object, integer, or None
A pseudo-random number generator. Typically will only
be specified if you have a reason to generate the same
set of random numbers, such as for a test. Default is None,
which sets the seed based on the system time.
quiet : boolean, optional
If True, log messages will not be displayed when
creating energies. Useful if you have to loop over
a lot of spectra. Default: False
"""
t_exp = parse_value(t_exp, "s")
fov = parse_value(fov, "arcmin")
prng = parse_prng(prng)
rate = fov*fov*self.total_flux.value
energy = _generate_energies(self, t_exp, rate, prng, quiet=quiet)
earea = self.arf.interpolate_area(energy).value
flux = np.sum(energy)*erg_per_keV/t_exp/earea.sum()
energies = Energies(energy, flux)
return energies
def _spectrum_init(self, kT, velocity, elem_abund):
kT = parse_value(kT, "keV")
velocity = parse_value(velocity, "km/s")
v = velocity*1.0e5
tindex = np.searchsorted(self.Tvals, kT)-1
dT = (kT-self.Tvals[tindex])/self.dTvals[tindex]
return kT, dT, tindex, v
def generate_energies(self, t_exp, fov, prng=None,
quiet=False):
"""
Generate photon energies from this convolved
background spectrum given an exposure time and
field of view.
Parameters
----------
t_exp : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The exposure time in seconds.
fov : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The width of the field of view on a side
in arcminutes.
prng : :class:`~numpy.random.RandomState` object, integer, or None
A pseudo-random number generator. Typically will only
be specified if you have a reason to generate the same
set of random numbers, such as for a test. Default is None,
which sets the seed based on the system time.
quiet : boolean, optional
If True, log messages will not be displayed when
creating energies. Useful if you have to loop over
a lot of spectra. Default: False
"""
t_exp = parse_value(t_exp, "s")
fov = parse_value(fov, "arcmin")
prng = parse_prng(prng)
rate = fov*fov*self.total_flux.value
energy = _generate_energies(self, t_exp, rate, prng, quiet=quiet)
earea = self.arf.interpolate_area(energy).value
flux = np.sum(energy)*erg_per_keV/t_exp/earea.sum()
energies = Energies(energy, flux)
return energies
def from_powerlaw(cls, photon_index, redshift, norm, emin, emax,
nbins):
"""
Create a spectrum from a power-law model.
Parameters
----------
photon_index : float
The photon index of the source.
redshift : float
The redshift of the source.
norm : float
The normalization of the source in units of
photons/s/cm**2/keV at 1 keV in the source
frame.
emin : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The minimum energy of the spectrum in keV.
emax : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The maximum energy of the spectrum in keV.
nbins : integer
The number of bins in the spectrum.
"""
emin = parse_value(emin, 'keV')
emax = parse_value(emax, 'keV')
ebins = np.linspace(emin, emax, nbins+1)
emid = 0.5*(ebins[1:]+ebins[:-1])
flux = norm*(emid*(1.0+redshift))**(-photon_index)
return cls(ebins, flux)
def _from_xspec(cls, xspec_in, emin, emax, nbins):
emin = parse_value(emin, "keV")
emax = parse_value(emax, "keV")
tmpdir = tempfile.mkdtemp()
curdir = os.getcwd()
os.chdir(tmpdir)
xspec_in.append("dummyrsp %g %g %d lin\n" % (emin, emax, nbins))
xspec_in += ["set fp [open spec_therm.xspec w+]\n",
"tclout energies\n", "puts $fp $xspec_tclout\n",
"tclout modval\n", "puts $fp $xspec_tclout\n",
"close $fp\n", "quit\n"]
f_xin = open("xspec.in", "w")
f_xin.writelines(xspec_in)
f_xin.close()
logfile = os.path.join(curdir, "xspec.log")
with open(logfile, "ab") as xsout:
subprocess.call(["xspec", "-", "xspec.in"],
stdout=xsout, stderr=xsout)
f_s = open("spec_therm.xspec", "r")
lines = f_s.readlines()
f_s.close()
ebins = np.array(lines[0].split()).astype("float64")
de = np.diff(ebins)[0]
flux = np.array(lines[1].split()).astype("float64")/de
os.chdir(curdir)
shutil.rmtree(tmpdir)
return cls(ebins, flux)
def from_powerlaw(cls, photon_index, redshift, norm,
emin=0.01, emax=50.0, nbins=10000):
"""
Create a spectrum from a power-law model.
Parameters
----------
photon_index : float
The photon index of the source.
redshift : float
The redshift of the source.
norm : float
The normalization of the source in units of
photons/s/cm**2/keV at 1 keV in the source
frame.
emin : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`, optional
The minimum energy of the spectrum in keV.
Default: 0.01
emax : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`, optional
The maximum energy of the spectrum in keV.
Default: 50.0
nbins : integer, optional
The number of bins in the spectrum. Default: 10000
"""
emin = parse_value(emin, 'keV')
emax = parse_value(emax, 'keV')
ebins = np.linspace(emin, emax, nbins+1)
emid = 0.5*(ebins[1:]+ebins[:-1])
flux = norm*(emid*(1.0+redshift))**(-photon_index)
return cls(ebins, flux)
def get_flux_in_band(self, emin, emax):
"""
Determine the total flux within a band specified
by an energy range.
Parameters
----------
emin : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The minimum energy in the band, in keV.
emax : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The maximum energy in the band, in keV.
Returns
-------
A tuple of values for the flux/intensity in the
band: the first value is in terms of the photon
rate, the second value is in terms of the energy rate.
"""
emin = parse_value(emin, "keV")
emax = parse_value(emax, "keV")
range = np.logical_and(self.emid.value >= emin,
self.emid.value <= emax)
pflux = self.flux[range].sum() * self.de
eflux = (self.flux *
self.emid.to("erg"))[range].sum() * self.de / (1.0 * u.photon)
return pflux, eflux
def _spectrum_init(self, kT, velocity, elem_abund):
kT = parse_value(kT, "keV")
velocity = parse_value(velocity, "km/s")
v = velocity*1.0e5
tindex = np.searchsorted(self.Tvals, kT)-1
dT = (kT-self.Tvals[tindex])/self.dTvals[tindex]
return kT, dT, tindex, v
def __init__(self,
ra0,
dec0,
r_in,
r_out,
num_events,
theta=0.0,
ellipticity=1.0,
prng=None):
r_in = parse_value(r_in, "arcsec")
r_out = parse_value(r_out, "arcsec")
def func(r):
f = np.zeros(r.size)
idxs = np.logical_and(r >= r_in, r < r_out)
f[idxs] = 1.0
return f
super(AnnulusModel, self).__init__(ra0,
dec0,
func,
num_events,
theta=theta,
ellipticity=ellipticity,
prng=prng)
def add_emission_line(self, line_center, line_width, line_amp,
line_type="gaussian"):
"""
Add an emission line to this spectrum.
Parameters
----------
line_center : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The line center position in units of keV, in the observer frame.
line_width : one or more float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The line width (FWHM) in units of keV, in the observer frame. Can also
input the line width in units of velocity in the rest frame. For the Voigt
profile, a list, tuple, or array of two values should be provided since there
are two line widths, the Lorentzian and the Gaussian (in that order).
line_amp : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The integrated line amplitude in the units of the flux
line_type : string, optional
The line profile type. Default: "gaussian"
"""
line_center = parse_value(line_center, "keV")
line_width = parse_value(line_width, "keV", equivalence=line_width_equiv(line_center))
line_amp = parse_value(line_amp, self._units)
if line_type == "gaussian":
sigma = line_width / sigma_to_fwhm
line_amp /= sqrt2pi * sigma
f = Gaussian1D(line_amp, line_center, sigma)
else:
raise NotImplementedError("Line profile type '%s' " % line_type +
"not implemented!")
self.flux += u.Quantity(f(self.emid.value), self._units)
self._compute_total_flux()
def __init__(self, ra0, dec0, num_events):
ra0 = parse_value(ra0, "deg")
dec0 = parse_value(dec0, "deg")
ra = ra0 * np.ones(num_events)
dec = dec0 * np.ones(num_events)
w = construct_wcs(ra0, dec0)
zero_pos = np.zeros(num_events)
super(PointSourceModel, self).__init__(ra, dec, zero_pos, zero_pos, w)
def __init__(self, ra0, dec0, r_c1, beta1, r_c2, beta2, sb_ratio,
theta=0.0, ellipticity=1.0):
r_c1 = parse_value(r_c1, "arcsec")
r_c2 = parse_value(r_c2, "arcsec")
func = lambda r: (1.0+(r/r_c1)**2)**(-3*beta1+0.5) + \
sb_ratio*(1.0+(r/r_c2)**2)**(-3*beta2+0.5)
super(DoubleBetaModel, self).__init__(ra0, dec0, func, theta=theta,
ellipticity=ellipticity)
def _new_spec_from_band(self, emin, emax):
emin = parse_value(emin, "keV")
emax = parse_value(emax, 'keV')
band = np.logical_and(self.ebins.value >= emin,
self.ebins.value <= emax)
idxs = np.where(band)[0]
ebins = self.ebins.value[idxs]
flux = self.flux.value[idxs[:-1]]
return ebins, flux
def to_scaled_spectrum(self, fov, focal_length=None):
from soxs.instrument import FlatResponse
fov = parse_value(fov, "arcmin")
if focal_length is None:
focal_length = self.default_focal_length
else:
focal_length = parse_value(focal_length, "m")
flux = self.flux.value * fov * fov
flux *= (focal_length / self.default_focal_length)**2
arf = FlatResponse(self.ebins.value[0], self.ebins.value[-1], 1.0,
self.ebins.size - 1)
return ConvolvedSpectrum(Spectrum(self.ebins.value, flux), arf)
def __init__(self, ra0, dec0, r_in, r_out, theta=0.0,
ellipticity=1.0):
r_in = parse_value(r_in, "arcsec")
r_out = parse_value(r_out, "arcsec")
def func(r):
f = np.zeros(r.size)
idxs = np.logical_and(r >= r_in, r < r_out)
f[idxs] = 1.0
return f
super(AnnulusModel, self).__init__(ra0, dec0, func,
theta=theta,
ellipticity=ellipticity)
def to_scaled_spectrum(self, fov, focal_length=None):
from soxs.instrument import FlatResponse
fov = parse_value(fov, "arcmin")
if focal_length is None:
focal_length = self.default_focal_length
else:
focal_length = parse_value(focal_length, "m")
flux = self.flux.value*fov*fov
flux *= (focal_length/self.default_focal_length)**2
arf = FlatResponse(self.ebins.value[0], self.ebins.value[-1],
1.0, self.ebins.size-1)
return ConvolvedSpectrum(Spectrum(self.ebins.value, flux), arf)
def apply_foreground_absorption(self, nH, model="wabs", redshift=0.0):
"""
Given a hydrogen column density, apply
galactic foreground absorption to the spectrum.
Parameters
----------
nH : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The hydrogen column in units of 10**22 atoms/cm**2
model : string, optional
The model for absorption to use. Options are "wabs"
(Wisconsin, Morrison and McCammon; ApJ 270, 119) or
"tbabs" (Tuebingen-Boulder, Wilms, J., Allen, A., &
McCray, R. 2000, ApJ, 542, 914). Default: "wabs".
redshift : float, optional
The redshift of the absorbing material. Default: 0.0
"""
nH = parse_value(nH, "1.0e22*cm**-2")
e = self.emid.value*(1.0+redshift)
if model == "wabs":
sigma = wabs_cross_section(e)
elif model == "tbabs":
sigma = tbabs_cross_section(e)
self.flux *= np.exp(-nH*1.0e22*sigma)
self._compute_total_flux()
def convolve_spectrum(self, cspec, exp_time, noisy=True, prng=None):
prng = parse_prng(prng)
exp_time = parse_value(exp_time, "s")
counts = cspec.flux.value * exp_time * cspec.de.value
spec = np.histogram(cspec.emid.value, self.ebins, weights=counts)[0]
conv_spec = np.zeros(self.n_ch)
pbar = tqdm(leave=True, total=self.n_e, desc="Convolving spectrum ")
if np.all(self.data["N_GRP"] == 1):
# We can do things a bit faster if there is only one group each
f_chan = ensure_numpy_array(np.nan_to_num(self.data["F_CHAN"]))
n_chan = ensure_numpy_array(np.nan_to_num(self.data["N_CHAN"]))
mat = np.nan_to_num(np.float64(self.data["MATRIX"]))
mat_size = np.minimum(n_chan, self.n_ch-f_chan)
for k in range(self.n_e):
conv_spec[f_chan[k]:f_chan[k]+n_chan[k]] += spec[k]*mat[k,:mat_size[k]]
pbar.update()
else:
# Otherwise, we have to go step-by-step
for k in range(self.n_e):
f_chan = ensure_numpy_array(np.nan_to_num(self.data["F_CHAN"][k]))
n_chan = ensure_numpy_array(np.nan_to_num(self.data["N_CHAN"][k]))
mat = np.nan_to_num(np.float64(self.data["MATRIX"][k]))
mat_size = np.minimum(n_chan, self.n_ch-f_chan)
for i, f in enumerate(f_chan):
conv_spec[f:f+n_chan[i]] += spec[k]*mat[:mat_size[i]]
pbar.update()
pbar.close()
if noisy:
return prng.poisson(lam=conv_spec)
else:
return conv_spec
def generate_sources(fov, sky_center, prng=None):
r"""
Make a catalog of point sources.
Parameters
----------
fov : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The field of view in arcminutes.
sky_center : array-like
The center RA, Dec of the field of view in degrees.
prng : :class:`~numpy.random.RandomState` object, integer, or None
A pseudo-random number generator. Typically will only
be specified if you have a reason to generate the same
set of random numbers, such as for a test. Default is None,
which sets the seed based on the system time.
"""
prng = parse_prng(prng)
fov = parse_value(fov, "arcmin")
agn_fluxes, gal_fluxes = generate_fluxes(fov, prng)
fluxes = np.concatenate([agn_fluxes, gal_fluxes])
ind = np.concatenate([
get_agn_index(np.log10(agn_fluxes)),
gal_index * np.ones(gal_fluxes.size)
])
ra0, dec0 = generate_positions(fluxes.size, fov, sky_center, prng)
return ra0, dec0, fluxes, ind
def apply_foreground_absorption(self, nH, model="wabs", redshift=0.0):
"""
Given a hydrogen column density, apply
galactic foreground absorption to the spectrum.
Parameters
----------
nH : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The hydrogen column in units of 10**22 atoms/cm**2
model : string, optional
The model for absorption to use. Options are "wabs"
(Wisconsin, Morrison and McCammon; ApJ 270, 119) or
"tbabs" (Tuebingen-Boulder, Wilms, J., Allen, A., &
McCray, R. 2000, ApJ, 542, 914). Default: "wabs".
redshift : float, optional
The redshift of the absorbing material. Default: 0.0
"""
nH = parse_value(nH, "1.0e22*cm**-2")
e = self.emid.value*(1.0+redshift)
if model == "wabs":
sigma = wabs_cross_section(e)
elif model == "tbabs":
sigma = tbabs_cross_section(e)
self.flux *= np.exp(-nH*1.0e22*sigma)
self._compute_total_flux()
def generate_fluxes(fov, prng):
from soxs.data import cdf_fluxes, cdf_gal, cdf_agn
prng = parse_prng(prng)
fov = parse_value(fov, "arcmin")
logf = np.log10(cdf_fluxes)
n_gal = np.rint(cdf_gal[-1])
n_agn = np.rint(cdf_agn[-1])
F_gal = cdf_gal / cdf_gal[-1]
F_agn = cdf_agn / cdf_agn[-1]
f_gal = InterpolatedUnivariateSpline(F_gal, logf)
f_agn = InterpolatedUnivariateSpline(F_agn, logf)
fov_area = fov**2
n_gal = int(n_gal * fov_area / 3600.0)
n_agn = int(n_agn * fov_area / 3600.0)
mylog.debug(f"{n_agn} AGN, {n_gal} galaxies in the FOV.")
randvec1 = prng.uniform(size=n_agn)
agn_fluxes = 10**f_agn(randvec1)
randvec2 = prng.uniform(size=n_gal)
gal_fluxes = 10**f_gal(randvec2)
return agn_fluxes, gal_fluxes
def get_spectrum(self, kT, abund, redshift, norm, velocity=0.0,
elem_abund=None):
"""
Get a thermal emission spectrum.
Parameters
----------
kT : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The temperature in keV.
abund : float
The metal abundance in solar units.
redshift : float
The redshift.
norm : float
The normalization of the model, in the standard
Xspec units of 1.0e-14*EM/(4*pi*(1+z)**2*D_A**2).
velocity : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`, optional
The velocity broadening parameter, in units of
km/s. Default: 0.0
elem_abund : dict of element name, float pairs
A dictionary of elemental abundances to vary
freely of the abund parameter. Default: None
"""
kT = parse_value(kT, "keV")
velocity = parse_value(velocity, "km/s")
v = velocity*1.0e5
if elem_abund is None:
elem_abund = {}
if set(elem_abund.keys()) != set(self.var_elem_names):
raise RuntimeError("The supplied set of abundances is not the "
"same as that was originally set!\n"
"Free elements: %s\nAbundances: %s" % (set(elem_abund.keys()),
set(self.var_elem_names)))
tindex = np.searchsorted(self.Tvals, kT)-1
if tindex >= self.Tvals.shape[0]-1 or tindex < 0:
return np.zeros(self.nbins)
dT = (kT-self.Tvals[tindex])/self.dTvals[tindex]
cspec, mspec, vspec = self._get_table([tindex, tindex+1], redshift, v)
cosmic_spec = cspec[0,:]*(1.-dT)+cspec[1,:]*dT
metal_spec = mspec[0,:]*(1.-dT)+mspec[1,:]*dT
spec = cosmic_spec + abund*metal_spec
if vspec is not None:
for elem, eabund in elem_abund.items():
j = self.var_elem_names.index(elem)
spec += eabund*(vspec[j,0,:]*(1.-dT)+vspec[j,1,:]*dT)
spec = 1.0e14*norm*spec/self.de
return Spectrum(self.ebins, spec)
def __init__(self, ra0, dec0, r_c, beta, theta=0.0, ellipticity=1.0):
r_c = parse_value(r_c, "arcsec")
func = lambda r: (1.0 + (r / r_c)**2)**(-3 * beta + 0.5)
super(BetaModel, self).__init__(ra0,
dec0,
func,
theta=theta,
ellipticity=ellipticity)
def __init__(self, emin, emax, nbins, var_elem=None, apec_root=None,
apec_vers="3.0.8", broadening=True, nolines=False):
emin = parse_value(emin, "keV")
emax = parse_value(emax, 'keV')
self.emin = emin
self.emax = emax
self.nbins = nbins
self.ebins = np.linspace(self.emin, self.emax, nbins+1)
self.de = np.diff(self.ebins)
self.emid = 0.5*(self.ebins[1:]+self.ebins[:-1])
if apec_root is None:
apec_root = soxs_files_path
self.cocofile = os.path.join(apec_root, "apec_v%s_coco.fits" % apec_vers)
self.linefile = os.path.join(apec_root, "apec_v%s_line.fits" % apec_vers)
if not os.path.exists(self.cocofile) or not os.path.exists(self.linefile):
raise IOError("Cannot find the APEC files!\n %s\n, %s" % (self.cocofile,
self.linefile))
self.nolines = nolines
self.wvbins = hc/self.ebins[::-1]
self.broadening = broadening
try:
self.line_handle = pyfits.open(self.linefile)
except IOError:
raise IOError("LINE file %s does not exist" % self.linefile)
try:
self.coco_handle = pyfits.open(self.cocofile)
except IOError:
raise IOError("COCO file %s does not exist" % self.cocofile)
self.Tvals = self.line_handle[1].data.field("kT")
self.nT = len(self.Tvals)
self.dTvals = np.diff(self.Tvals)
self.minlam = self.wvbins.min()
self.maxlam = self.wvbins.max()
if var_elem is None:
self.var_elem = []
else:
self.var_elem = [elem_names.index(elem) for elem in var_elem]
self.var_elem.sort()
self.var_elem_names = [elem_names[elem] for elem in self.var_elem]
self.num_var_elem = len(self.var_elem)
self.cosmic_elem = [elem for elem in cosmic_elem
if elem not in self.var_elem]
self.metal_elem = [elem for elem in metal_elem
if elem not in self.var_elem]
def generate_sources(exp_time, fov, sky_center, area=40000.0, prng=None):
r"""
Make a catalog of point sources.
Parameters
----------
exp_time : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The exposure time of the observation in seconds.
fov : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The field of view in arcminutes.
sky_center : array-like
The center RA, Dec of the field of view in degrees.
area : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`, optional
The effective area in cm**2. It must be large enough
so that a sufficiently large sample is drawn for the
ARF. Default: 40000.
prng : :class:`~numpy.random.RandomState` object, integer, or None
A pseudo-random number generator. Typically will only
be specified if you have a reason to generate the same
set of random numbers, such as for a test. Default is None,
which sets the seed based on the system time.
"""
prng = parse_prng(prng)
exp_time = parse_value(exp_time, "s")
fov = parse_value(fov, "arcmin")
area = parse_value(area, "cm**2")
agn_fluxes, gal_fluxes = generate_fluxes(exp_time, area, fov, prng)
fluxes = np.concatenate([agn_fluxes, gal_fluxes])
ind = np.concatenate([get_agn_index(np.log10(agn_fluxes)),
gal_index * np.ones(gal_fluxes.size)])
dec_scal = np.fabs(np.cos(sky_center[1] * np.pi / 180))
ra_min = sky_center[0] - fov / (2.0 * 60.0 * dec_scal)
dec_min = sky_center[1] - fov / (2.0 * 60.0)
ra0 = prng.uniform(size=fluxes.size) * fov / (60.0 * dec_scal) + ra_min
dec0 = prng.uniform(size=fluxes.size) * fov / 60.0 + dec_min
return ra0, dec0, fluxes, ind
def __init__(self, ra0, dec0, fov, num_events, prng=None):
fov = parse_value(fov, "arcmin")
width = fov * 60.0
height = fov * 60.0
super(FillFOVModel, self).__init__(ra0,
dec0,
width,
height,
num_events,
prng=prng)
def __init__(self,
ra0,
dec0,
width,
height,
num_events,
theta=0.0,
prng=None):
prng = parse_prng(prng)
ra0 = parse_value(ra0, "deg")
dec0 = parse_value(dec0, "deg")
width = parse_value(width, "arcsec")
height = parse_value(height, "arcsec")
w = construct_wcs(ra0, dec0)
x = prng.uniform(low=-0.5 * width, high=0.5 * width, size=num_events)
y = prng.uniform(low=-0.5 * height, high=0.5 * height, size=num_events)
coords = rotate_xy(theta, x, y)
ra, dec = w.wcs_pix2world(coords[0, :], coords[1, :], 1)
super(RectangleModel, self).__init__(ra, dec, coords[0, :],
coords[1, :], w)
def new_spec_from_band(self, emin, emax):
"""
Create a new :class:`~soxs.spectra.Spectrum` object
from a subset of an existing one defined by a particular
energy band.
Parameters
----------
emin : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The minimum energy of the band in keV.
emax : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The maximum energy of the band in keV.
"""
emin = parse_value(emin, "keV")
emax = parse_value(emax, 'keV')
band = np.logical_and(self.ebins.value >= emin,
self.ebins.value <= emax)
idxs = np.where(band)[0]
ebins = self.ebins.value[idxs]
flux = self.flux.value[idxs[:-1]]
return Spectrum(ebins, flux)
def __init__(self,
ra0,
dec0,
func,
num_events,
theta=0.0,
ellipticity=1.0,
prng=None):
prng = parse_prng(prng)
ra0 = parse_value(ra0, "deg")
dec0 = parse_value(dec0, "deg")
theta = parse_value(theta, "deg")
x, y = generate_radial_events(num_events,
func,
prng,
ellipticity=ellipticity)
w = construct_wcs(ra0, dec0)
coords = rotate_xy(theta, x, y)
ra, dec = w.wcs_pix2world(coords[0, :], coords[1, :], 1)
super(RadialFunctionModel, self).__init__(ra, dec, coords[0, :],
coords[1, :], w)
def new_spec_from_band(self, emin, emax):
"""
Create a new :class:`~soxs.spectra.Spectrum` object
from a subset of an existing one defined by a particular
energy band.
Parameters
----------
emin : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The minimum energy of the band in keV.
emax : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The maximum energy of the band in keV.
"""
emin = parse_value(emin, "keV")
emax = parse_value(emax, 'keV')
band = np.logical_and(self.ebins.value >= emin,
self.ebins.value <= emax)
idxs = np.where(band)[0]
ebins = self.ebins.value[idxs]
flux = self.flux.value[idxs[:-1]]
return Spectrum(ebins, flux)
def from_models(cls,
name,
spectral_model,
spatial_model,
t_exp,
area,
prng=None):
"""
Generate a single photon list from a spectral and a spatial
model.
Parameters
----------
name : string
The name of the photon list. This will also be the prefix
of any photon list file that is written from this photon list.
spectral_model : :class:`~soxs.spectra.Spectrum`
The spectral model to use to generate the event energies.
spatial_model : :class:`~soxs.spatial.SpatialModel`
The spatial model to use to generate the event coordinates.
t_exp : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The exposure time in seconds.
area : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The effective area in cm**2. If one is creating
events for a SIMPUT file, a constant should be
used and it must be large enough so that a
sufficiently large sample is drawn for the ARF.
prng : :class:`~numpy.random.RandomState` object, integer, or None
A pseudo-random number generator. Typically will only
be specified if you have a reason to generate the same
set of random numbers, such as for a test. Default is None,
which sets the seed based on the system time.
"""
prng = parse_prng(prng)
t_exp = parse_value(t_exp, "s")
area = parse_value(area, "cm**2")
e = spectral_model.generate_energies(t_exp, area, prng=prng)
ra, dec = spatial_model.generate_coords(e.size, prng=prng)
return cls(name, ra, dec, e, e.flux)
def from_constant(cls, const_flux, emin, emax, nbins):
"""
Create a spectrum from a constant model using
XSPEC.
Parameters
----------
const_flux : float
The value of the constant flux in the units
of the spectrum.
emin : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The minimum energy of the spectrum in keV.
emax : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The maximum energy of the spectrum in keV.
nbins : integer
The number of bins in the spectrum.
"""
emin = parse_value(emin, "keV")
emax = parse_value(emax, 'keV')
ebins = np.linspace(emin, emax, nbins+1)
flux = const_flux*np.ones(nbins)
return cls(ebins, flux)
def from_constant(cls, const_flux, emin, emax, nbins):
"""
Create a spectrum from a constant model using
XSPEC.
Parameters
----------
const_flux : float
The value of the constant flux in the units
of the spectrum.
emin : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The minimum energy of the spectrum in keV.
emax : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The maximum energy of the spectrum in keV.
nbins : integer
The number of bins in the spectrum.
"""
emin = parse_value(emin, "keV")
emax = parse_value(emax, 'keV')
ebins = np.linspace(emin, emax, nbins+1)
flux = const_flux*np.ones(nbins)
return cls(ebins, flux)
def make_simple_instrument(base_inst,
new_inst,
fov,
num_pixels,
no_bkgnd=False,
no_psf=False,
no_dither=False):
"""
Using an existing imaging instrument specification,
make a simple square instrument given a field of view
and a resolution.
Parameters
----------
base_inst : string
The name for the instrument specification to base the
new one on.
new_inst : string
The name for the new instrument specification.
fov : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The field of view in arcminutes.
num_pixels : integer
The number of pixels on a side.
no_bkgnd : boolean, optional
Set this new instrument to have no particle background.
Default: False
no_psf : boolean, optional
Set this new instrument to have no spatial PSF.
Default: False
no_dither : boolean, optional
Set this new instrument to have no dithering.
Default: False
"""
sq_inst = get_instrument_from_registry(base_inst)
if sq_inst["imaging"] is False:
raise RuntimeError("make_simple_instrument only works with "
"imaging instruments!")
sq_inst["name"] = new_inst
sq_inst["chips"] = None
sq_inst["fov"] = parse_value(fov, "arcmin")
sq_inst["num_pixels"] = num_pixels
if no_bkgnd:
sq_inst["bkgnd"] = None
elif base_inst.startswith("aciss"):
# Special-case ACIS-S to use the BI background on S3
sq_inst["bkgnd"] = "aciss"
if no_psf:
sq_inst["psf"] = None
if sq_inst["dither"]:
sq_inst["dither"] = not no_dither
add_instrument_to_registry(sq_inst)
def get_flux_in_band(self, emin, emax):
"""
Determine the total flux within a band specified
by an energy range.
Parameters
----------
emin : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The minimum energy in the band, in keV.
emax : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The maximum energy in the band, in keV.
Returns
-------
A tuple of values for the flux/intensity in the
band: the first value is in terms of the photon
rate, the second value is in terms of the energy rate.
"""
emin = parse_value(emin, "keV")
emax = parse_value(emax, "keV")
range = np.logical_and(self.emid.value >= emin, self.emid.value <= emax)
pflux = self.flux[range].sum()*self.de
eflux = (self.flux*self.emid.to("erg"))[range].sum()*self.de/(1.0*u.photon)
return pflux, eflux
def make_simple_instrument(base_inst, new_inst, fov, num_pixels,
no_bkgnd=False, no_psf=False, no_dither=False):
"""
Using an existing imaging instrument specification,
make a simple square instrument given a field of view
and a resolution.
Parameters
----------
base_inst : string
The name for the instrument specification to base the
new one on.
new_inst : string
The name for the new instrument specification.
fov : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The field of view in arcminutes.
num_pixels : integer
The number of pixels on a side.
no_bkgnd : boolean, optional
Set this new instrument to have no particle background.
Default: False
no_psf : boolean, optional
Set this new instrument to have no spatial PSF.
Default: False
no_dither : boolean, optional
Set this new instrument to have no dithering.
Default: False
"""
sq_inst = get_instrument_from_registry(base_inst)
if sq_inst["imaging"] is False:
raise RuntimeError("make_simple_instrument only works with "
"imaging instruments!")
sq_inst["name"] = new_inst
sq_inst["chips"] = None
sq_inst["fov"] = parse_value(fov, "arcmin")
sq_inst["num_pixels"] = num_pixels
if no_bkgnd:
sq_inst["bkgnd"] = None
elif base_inst.startswith("aciss"):
# Special-case ACIS-S to use the BI background on S3
sq_inst["bkgnd"] = "aciss"
if no_psf:
sq_inst["psf"] = None
if sq_inst["dither"]:
sq_inst["dither"] = not no_dither
add_instrument_to_registry(sq_inst)
def convolve_spectrum(self, cspec, exp_time, prng=None):
prng = parse_prng(prng)
exp_time = parse_value(exp_time, "s")
counts = cspec.flux.value * exp_time * cspec.de.value
spec = np.histogram(cspec.emid.value, self.ebins, weights=counts)[0]
conv_spec = np.zeros(self.n_ch)
pbar = tqdm(leave=True, total=self.n_e, desc="Convolving spectrum ")
for k in range(self.n_e):
f_chan = ensure_numpy_array(np.nan_to_num(self.data["F_CHAN"][k]))
n_chan = ensure_numpy_array(np.nan_to_num(self.data["N_CHAN"][k]))
mat = np.nan_to_num(np.float64(self.data["MATRIX"][k]))
for f, n in zip(f_chan, n_chan):
mat_size = min(n, self.n_ch-f)
conv_spec[f:f+n] += spec[k]*mat[:mat_size]
pbar.update()
pbar.close()
return prng.poisson(lam=conv_spec)
def from_spectrum(cls, spec, fov):
"""
Create a background spectrum from a regular
:class:`~soxs.spectra.Spectrum` object and the width
of a field of view on a side.
Parameters
----------
spec : :class:`~soxs.spectra.Spectrum`
The spectrum to be used.
fov : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The width of the field of view on a side in
arcminutes.
"""
fov = parse_value(fov, "arcmin")
flux = spec.flux.value/fov/fov
return cls(spec.flux.ebins.value, flux)
def simulate_spectrum(spec, instrument, exp_time, out_file,
instr_bkgnd=False, foreground=False,
ptsrc_bkgnd=False, bkgnd_area=None,
absorb_model="wabs", nH=0.05,
overwrite=False, prng=None):
"""
Generate a PI or PHA spectrum from a :class:`~soxs.spectra.Spectrum`
by convolving it with responses. To be used if one wants to
create a spectrum without worrying about spatial response. Similar
to XSPEC's "fakeit".
Parameters
----------
spec : :class:`~soxs.spectra.Spectrum`
The spectrum to be convolved. If None is supplied, only backgrounds
will be simulated (if they are turned on).
instrument : string
The name of the instrument to use, which picks an instrument
specification from the instrument registry.
exp_time : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The exposure time in seconds.
out_file : string
The file to write the spectrum to.
instr_bkgnd : boolean, optional
Whether or not to include the instrumental/particle background.
Default: False
foreground : boolean, optional
Whether or not to include the local foreground.
Default: False
ptsrc_bkgnd : boolean, optional
Whether or not to include the unresolved point-source background.
Default: False
bkgnd_area : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The area on the sky for the background components, in square arcminutes.
Default: None, necessary to specify if any of the background components
are turned on.
absorb_model : string, optional
The absorption model to use, "wabs" or "tbabs". Default: "wabs"
nH : float, optional
The hydrogen column in units of 10**22 atoms/cm**2.
Default: 0.05
overwrite : boolean, optional
Whether or not to overwrite an existing file. Default: False
prng : :class:`~numpy.random.RandomState` object, integer, or None
A pseudo-random number generator. Typically will only
be specified if you have a reason to generate the same
set of random numbers, such as for a test. Default is None,
which sets the seed based on the system time.
Examples
--------
>>> spec = soxs.Spectrum.from_file("my_spectrum.txt")
>>> soxs.simulate_spectrum(spec, "lynx_lxm", 100000.0,
... "my_spec.pi", overwrite=True)
"""
from soxs.events import _write_spectrum
from soxs.instrument import RedistributionMatrixFile, \
AuxiliaryResponseFile
from soxs.spectra import ConvolvedSpectrum
from soxs.background.foreground import hm_astro_bkgnd
from soxs.background.instrument import instrument_backgrounds
from soxs.background.spectra import BackgroundSpectrum, \
ConvolvedBackgroundSpectrum
prng = parse_prng(prng)
exp_time = parse_value(exp_time, "s")
try:
instrument_spec = instrument_registry[instrument]
except KeyError:
raise KeyError("Instrument %s is not in the instrument registry!" % instrument)
if foreground or instr_bkgnd or ptsrc_bkgnd:
if instrument_spec["grating"]:
raise NotImplementedError("Backgrounds cannot be included in simulations "
"of gratings spectra at this time!")
if bkgnd_area is None:
raise RuntimeError("The 'bkgnd_area' argument must be set if one wants "
"to simulate backgrounds! Specify a value in square "
"arcminutes.")
bkgnd_area = np.sqrt(parse_value(bkgnd_area, "arcmin**2"))
elif spec is None:
raise RuntimeError("You have specified no source spectrum and no backgrounds!")
arf_file = get_response_path(instrument_spec["arf"])
rmf_file = get_response_path(instrument_spec["rmf"])
arf = AuxiliaryResponseFile(arf_file)
rmf = RedistributionMatrixFile(rmf_file)
event_params = {}
event_params["RESPFILE"] = os.path.split(rmf.filename)[-1]
event_params["ANCRFILE"] = os.path.split(arf.filename)[-1]
event_params["TELESCOP"] = rmf.header["TELESCOP"]
event_params["INSTRUME"] = rmf.header["INSTRUME"]
event_params["MISSION"] = rmf.header.get("MISSION", "")
out_spec = np.zeros(rmf.n_ch)
if spec is not None:
cspec = ConvolvedSpectrum(spec, arf)
out_spec += rmf.convolve_spectrum(cspec, exp_time, prng=prng)
fov = None if bkgnd_area is None else np.sqrt(bkgnd_area)
if foreground:
mylog.info("Adding in astrophysical foreground.")
cspec_frgnd = ConvolvedSpectrum(hm_astro_bkgnd.to_spectrum(fov), arf)
out_spec += rmf.convolve_spectrum(cspec_frgnd, exp_time, prng=prng)
if instr_bkgnd and instrument_spec["bkgnd"] is not None:
mylog.info("Adding in instrumental background.")
instr_spec = instrument_backgrounds[instrument_spec["bkgnd"]]
cspec_instr = instr_spec.to_scaled_spectrum(fov,
instrument_spec["focal_length"])
out_spec += rmf.convolve_spectrum(cspec_instr, exp_time, prng=prng)
if ptsrc_bkgnd:
mylog.info("Adding in background from unresolved point-sources.")
spec_plaw = BackgroundSpectrum.from_powerlaw(1.45, 0.0, 2.0e-7, emin=0.01,
emax=10.0, nbins=300000)
spec_plaw.apply_foreground_absorption(nH, model=absorb_model)
cspec_plaw = ConvolvedBackgroundSpectrum(spec_plaw.to_spectrum(fov), arf)
out_spec += rmf.convolve_spectrum(cspec_plaw, exp_time, prng=prng)
bins = (np.arange(rmf.n_ch)+rmf.cmin).astype("int32")
_write_spectrum(bins, out_spec, exp_time, rmf.header["CHANTYPE"],
event_params, out_file, overwrite=overwrite)
def make_background(exp_time, instrument, sky_center, foreground=True,
ptsrc_bkgnd=True, instr_bkgnd=True, no_dither=False,
dither_params=None, roll_angle=0.0, subpixel_res=False,
input_sources=None, absorb_model="wabs", nH=0.05, prng=None):
"""
Make background events.
Parameters
----------
exp_time : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The exposure time to use, in seconds.
instrument : string
The name of the instrument to use, which picks an instrument
specification from the instrument registry.
sky_center : array, tuple, or list
The center RA, Dec coordinates of the observation, in degrees.
foreground : boolean, optional
Whether or not to include the Galactic foreground. Default: True
instr_bkgnd : boolean, optional
Whether or not to include the instrumental background. Default: True
no_dither : boolean, optional
If True, turn off dithering entirely. Default: False
dither_params : array-like of floats, optional
The parameters to use to control the size and period of the dither
pattern. The first two numbers are the dither amplitude in x and y
detector coordinates in arcseconds, and the second two numbers are
the dither period in x and y detector coordinates in seconds.
Default: [8.0, 8.0, 1000.0, 707.0].
ptsrc_bkgnd : boolean, optional
Whether or not to include the point-source background. Default: True
Default: 0.05
roll_angle : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`, optional
The roll angle of the observation in degrees. Default: 0.0
subpixel_res: boolean, optional
If True, event positions are not randomized within the pixels
within which they are detected. Default: False
input_sources : string, optional
If set to a filename, input the point source positions, fluxes,
and spectral indices from an ASCII table instead of generating
them. Default: None
absorb_model : string, optional
The absorption model to use, "wabs" or "tbabs". Default: "wabs"
nH : float, optional
The hydrogen column in units of 10**22 atoms/cm**2.
Default: 0.05
prng : :class:`~numpy.random.RandomState` object, integer, or None
A pseudo-random number generator. Typically will only
be specified if you have a reason to generate the same
set of random numbers, such as for a test. Default is None,
which sets the seed based on the system time.
"""
from soxs.background import make_instrument_background, \
make_foreground, make_ptsrc_background
prng = parse_prng(prng)
exp_time = parse_value(exp_time, "s")
roll_angle = parse_value(roll_angle, "deg")
try:
instrument_spec = instrument_registry[instrument]
except KeyError:
raise KeyError("Instrument %s is not in the instrument registry!" % instrument)
if not instrument_spec["imaging"]:
raise RuntimeError("Instrument '%s' is not " % instrument_spec["name"] +
"designed for imaging observations!")
fov = instrument_spec["fov"]
input_events = defaultdict(list)
arf_file = get_response_path(instrument_spec["arf"])
arf = AuxiliaryResponseFile(arf_file)
rmf_file = get_response_path(instrument_spec["rmf"])
rmf = RedistributionMatrixFile(rmf_file)
if ptsrc_bkgnd:
mylog.info("Adding in point-source background.")
ptsrc_events = make_ptsrc_background(exp_time, fov, sky_center,
area=1.2*arf.max_area,
input_sources=input_sources,
absorb_model=absorb_model,
nH=nH, prng=prng)
for key in ["ra", "dec", "energy"]:
input_events[key].append(ptsrc_events[key])
input_events["flux"].append(ptsrc_events["flux"])
input_events["emin"].append(ptsrc_events["energy"].min())
input_events["emax"].append(ptsrc_events["energy"].max())
input_events["sources"].append("ptsrc_bkgnd")
events, event_params = generate_events(input_events, exp_time,
instrument, sky_center,
no_dither=no_dither,
dither_params=dither_params,
roll_angle=roll_angle,
subpixel_res=subpixel_res,
prng=prng)
mylog.info("Generated %d photons from the point-source background." % len(events["energy"]))
else:
nx = instrument_spec["num_pixels"]
events = defaultdict(list)
if not instrument_spec["dither"]:
dither_on = False
else:
dither_on = not no_dither
if dither_params is None:
dither_params = [8.0, 8.0, 1000.0, 707.0]
dither_dict = {"x_amp": dither_params[0],
"y_amp": dither_params[1],
"x_period": dither_params[2],
"y_period": dither_params[3],
"dither_on": dither_on,
"plate_scale": instrument_spec["fov"]/nx*60.0}
event_params = {"exposure_time": exp_time,
"fov": instrument_spec["fov"],
"num_pixels": nx,
"pix_center": np.array([0.5*(2*nx+1)]*2),
"channel_type": rmf.header["CHANTYPE"],
"sky_center": sky_center,
"dither_params": dither_dict,
"plate_scale": instrument_spec["fov"]/nx/60.0,
"chan_lim": [rmf.cmin, rmf.cmax],
"rmf": rmf_file, "arf": arf_file,
"telescope": rmf.header["TELESCOP"],
"instrument": instrument_spec['name'],
"mission": rmf.header.get("MISSION", ""),
"nchan": rmf.n_ch,
"roll_angle": roll_angle,
"aimpt_coords": instrument_spec["aimpt_coords"]}
if "chips" not in event_params:
event_params["chips"] = instrument_spec["chips"]
if foreground:
mylog.info("Adding in astrophysical foreground.")
bkg_events = make_foreground(event_params, arf, rmf, prng=prng)
for key in bkg_events:
events[key] = np.concatenate([events[key], bkg_events[key]])
if instr_bkgnd and instrument_spec["bkgnd"] is not None:
mylog.info("Adding in instrumental background.")
bkg_events = make_instrument_background(instrument_spec["bkgnd"],
event_params, rmf, prng=prng)
for key in bkg_events:
events[key] = np.concatenate([events[key], bkg_events[key]])
return events, event_params
def __init__(self, emin, emax, nbins, var_elem=None, apec_root=None,
apec_vers=None, broadening=True, nolines=False,
abund_table=None, nei=False):
if apec_vers is None:
filedir = os.path.join(os.path.dirname(__file__), 'files')
cfile = glob.glob("%s/apec_*_coco.fits" % filedir)[0]
apec_vers = cfile.split("/")[-1].split("_")[1][1:]
mylog.info("Using APEC version %s." % apec_vers)
if nei and apec_root is None:
raise RuntimeError("The NEI APEC tables are not supplied with "
"SOXS! Download them from http://www.atomdb.org "
"and set 'apec_root' to their location.")
if nei and var_elem is None:
raise RuntimeError("For NEI spectra, you must specify which elements "
"you want to vary using the 'var_elem' argument!")
self.nei = nei
emin = parse_value(emin, "keV")
emax = parse_value(emax, 'keV')
self.emin = emin
self.emax = emax
self.nbins = nbins
self.ebins = np.linspace(self.emin, self.emax, nbins+1)
self.de = np.diff(self.ebins)
self.emid = 0.5*(self.ebins[1:]+self.ebins[:-1])
if apec_root is None:
apec_root = soxs_files_path
if nei:
neistr = "_nei"
ftype = "comp"
else:
neistr = ""
ftype = "coco"
self.cocofile = os.path.join(apec_root, "apec_v%s%s_%s.fits" % (apec_vers, neistr, ftype))
self.linefile = os.path.join(apec_root, "apec_v%s%s_line.fits" % (apec_vers, neistr))
if not os.path.exists(self.cocofile) or not os.path.exists(self.linefile):
raise IOError("Cannot find the APEC files!\n %s\n, %s" % (self.cocofile,
self.linefile))
mylog.info("Using %s for generating spectral lines." % os.path.split(self.linefile)[-1])
mylog.info("Using %s for generating the continuum." % os.path.split(self.cocofile)[-1])
self.nolines = nolines
self.wvbins = hc/self.ebins[::-1]
self.broadening = broadening
try:
self.line_handle = pyfits.open(self.linefile)
except IOError:
raise IOError("Line file %s does not exist" % self.linefile)
try:
self.coco_handle = pyfits.open(self.cocofile)
except IOError:
raise IOError("Continuum file %s does not exist" % self.cocofile)
self.Tvals = self.line_handle[1].data.field("kT")
self.nT = len(self.Tvals)
self.dTvals = np.diff(self.Tvals)
self.minlam = self.wvbins.min()
self.maxlam = self.wvbins.max()
self.var_elem_names = []
self.var_ion_names = []
if var_elem is None:
self.var_elem = np.empty((0,1), dtype='int')
else:
self.var_elem = []
if len(var_elem) != len(set(var_elem)):
raise RuntimeError("Duplicates were found in the \"var_elem\" list! %s" % var_elem)
for elem in var_elem:
if "^" in elem:
if not self.nei:
raise RuntimeError("Cannot use different ionization states with a "
"CIE plasma!")
el = elem.split("^")
e = el[0]
ion = int(el[1])
else:
if self.nei:
raise RuntimeError("Variable elements must include the ionization "
"state for NEI plasmas!")
e = elem
ion = 0
self.var_elem.append([elem_names.index(e), ion])
self.var_elem.sort(key=lambda x: (x[0], x[1]))
self.var_elem = np.array(self.var_elem, dtype='int')
self.var_elem_names = [elem_names[e[0]] for e in self.var_elem]
self.var_ion_names = ["%s^%d" % (elem_names[e[0]], e[1]) for e in self.var_elem]
self.num_var_elem = len(self.var_elem)
if self.nei:
self.cosmic_elem = [elem for elem in [1, 2]
if elem not in self.var_elem[:, 0]]
self.metal_elem = []
else:
self.cosmic_elem = [elem for elem in cosmic_elem
if elem not in self.var_elem[:,0]]
self.metal_elem = [elem for elem in metal_elem
if elem not in self.var_elem[:,0]]
if abund_table is None:
abund_table = soxs_cfg.get("soxs", "abund_table")
if not isinstance(abund_table, string_types):
if len(abund_table) != 30:
raise RuntimeError("User-supplied abundance tables "
"must be 30 elements long!")
self.atable = np.concatenate([[0.0], np.array(abund_table)])
else:
self.atable = abund_tables[abund_table].copy()
self._atable = self.atable.copy()
self._atable[1:] /= abund_tables["angr"][1:]
def __init__(self, ra0, dec0, func, theta=0.0, ellipticity=1.0):
super(RadialFunctionModel, self).__init__(ra0, dec0)
self.theta = parse_value(theta, "deg")
self.func = func
self.ellipticity = ellipticity
def __init__(self, ra0, dec0, width, height, theta=0.0):
super(RectangleModel, self).__init__(ra0, dec0)
self.width = parse_value(width, "arcsec")
self.height = parse_value(height, "arcsec")
self.theta = parse_value(theta, "deg")
def __init__(self, ra0, dec0, fov):
fov = parse_value(fov, "arcmin")
width = fov*60.0
height = fov*60.0
super(FillFOVModel, self).__init__(ra0, dec0, width, height)
def __init__(self, ra0, dec0, r_c, beta, theta=0.0,
ellipticity=1.0):
r_c = parse_value(r_c, "arcsec")
func = lambda r: (1.0+(r/r_c)**2)**(-3*beta+0.5)
super(BetaModel, self).__init__(ra0, dec0, func, theta=theta,
ellipticity=ellipticity)
def generate_events(input_events, exp_time, instrument, sky_center,
no_dither=False, dither_params=None,
roll_angle=0.0, subpixel_res=False, prng=None):
"""
Take unconvolved events and convolve them with instrumental responses. This
function does the following:
1. Determines which events are observed using the ARF
2. Pixelizes the events, applying PSF effects and dithering
3. Determines energy channels using the RMF
This function is not meant to be called by the end-user but is used by
the :func:`~soxs.instrument.instrument_simulator` function.
Parameters
----------
input_events : string, dict, or None
The unconvolved events to be used as input. Can be one of the
following:
1. The name of a SIMPUT catalog file.
2. A Python dictionary containing the following items:
"ra": A NumPy array of right ascension values in degrees.
"dec": A NumPy array of declination values in degrees.
"energy": A NumPy array of energy values in keV.
"flux": The flux of the entire source, in units of erg/cm**2/s.
out_file : string
The name of the event file to be written.
exp_time : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`
The exposure time to use, in seconds.
instrument : string
The name of the instrument to use, which picks an instrument
specification from the instrument registry.
sky_center : array, tuple, or list
The center RA, Dec coordinates of the observation, in degrees.
no_dither : boolean, optional
If True, turn off dithering entirely. Default: False
dither_params : array-like of floats, optional
The parameters to use to control the size and period of the dither
pattern. The first two numbers are the dither amplitude in x and y
detector coordinates in arcseconds, and the second two numbers are
the dither period in x and y detector coordinates in seconds.
Default: [8.0, 8.0, 1000.0, 707.0].
roll_angle : float, (value, unit) tuple, or :class:`~astropy.units.Quantity`, optional
The roll angle of the observation in degrees. Default: 0.0
subpixel_res: boolean, optional
If True, event positions are not randomized within the pixels
within which they are detected. Default: False
prng : :class:`~numpy.random.RandomState` object, integer, or None
A pseudo-random number generator. Typically will only
be specified if you have a reason to generate the same
set of random numbers, such as for a test. Default is None,
which sets the seed based on the system time.
"""
import pyregion._region_filter as rfilter
exp_time = parse_value(exp_time, "s")
roll_angle = parse_value(roll_angle, "deg")
prng = parse_prng(prng)
if isinstance(input_events, dict):
parameters = {}
for key in ["flux", "emin", "emax", "sources"]:
parameters[key] = input_events[key]
event_list = []
for i in range(len(parameters["flux"])):
edict = {}
for key in ["ra", "dec", "energy"]:
edict[key] = input_events[key][i]
event_list.append(edict)
elif isinstance(input_events, string_types):
# Assume this is a SIMPUT catalog
event_list, parameters = read_simput_catalog(input_events)
try:
instrument_spec = instrument_registry[instrument]
except KeyError:
raise KeyError("Instrument %s is not in the instrument registry!" % instrument)
if not instrument_spec["imaging"]:
raise RuntimeError("Instrument '%s' is not " % instrument_spec["name"] +
"designed for imaging observations!")
arf_file = get_response_path(instrument_spec["arf"])
rmf_file = get_response_path(instrument_spec["rmf"])
arf = AuxiliaryResponseFile(arf_file)
rmf = RedistributionMatrixFile(rmf_file)
nx = instrument_spec["num_pixels"]
plate_scale = instrument_spec["fov"]/nx/60. # arcmin to deg
plate_scale_arcsec = plate_scale * 3600.0
if not instrument_spec["dither"]:
dither_on = False
else:
dither_on = not no_dither
if dither_params is None:
dither_params = [8.0, 8.0, 1000.0, 707.0]
dither_dict = {"x_amp": dither_params[0],
"y_amp": dither_params[1],
"x_period": dither_params[2],
"y_period": dither_params[3],
"dither_on": dither_on,
"plate_scale": plate_scale_arcsec}
event_params = {}
event_params["exposure_time"] = exp_time
event_params["arf"] = arf.filename
event_params["sky_center"] = sky_center
event_params["pix_center"] = np.array([0.5*(2*nx+1)]*2)
event_params["num_pixels"] = nx
event_params["plate_scale"] = plate_scale
event_params["rmf"] = rmf.filename
event_params["channel_type"] = rmf.header["CHANTYPE"]
event_params["telescope"] = rmf.header["TELESCOP"]
event_params["instrument"] = instrument_spec['name']
event_params["mission"] = rmf.header.get("MISSION", "")
event_params["nchan"] = rmf.n_ch
event_params["roll_angle"] = roll_angle
event_params["fov"] = instrument_spec["fov"]
event_params["chan_lim"] = [rmf.cmin, rmf.cmax]
event_params["chips"] = instrument_spec["chips"]
event_params["dither_params"] = dither_dict
event_params["aimpt_coords"] = instrument_spec["aimpt_coords"]
w = pywcs.WCS(naxis=2)
w.wcs.crval = event_params["sky_center"]
w.wcs.crpix = event_params["pix_center"]
w.wcs.cdelt = [-plate_scale, plate_scale]
w.wcs.ctype = ["RA---TAN","DEC--TAN"]
w.wcs.cunit = ["deg"]*2
rot_mat = get_rot_mat(roll_angle)
all_events = defaultdict(list)
for i, evts in enumerate(event_list):
mylog.info("Detecting events from source %s." % parameters["sources"][i])
# Step 1: Use ARF to determine which photons are observed
mylog.info("Applying energy-dependent effective area from %s." % os.path.split(arf.filename)[-1])
refband = [parameters["emin"][i], parameters["emax"][i]]
events = arf.detect_events(evts, exp_time, parameters["flux"][i], refband, prng=prng)
n_evt = events["energy"].size
if n_evt == 0:
mylog.warning("No events were observed for this source!!!")
else:
# Step 2: Assign pixel coordinates to events. Apply dithering and
# PSF. Clip events that don't fall within the detection region.
mylog.info("Pixeling events.")
# Convert RA, Dec to pixel coordinates
xpix, ypix = w.wcs_world2pix(events["ra"], events["dec"], 1)
xpix -= event_params["pix_center"][0]
ypix -= event_params["pix_center"][1]
events.pop("ra")
events.pop("dec")
n_evt = xpix.size
# Rotate physical coordinates to detector coordinates
det = np.dot(rot_mat, np.array([xpix, ypix]))
detx = det[0,:] + event_params["aimpt_coords"][0]
dety = det[1,:] + event_params["aimpt_coords"][1]
# Add times to events
events['time'] = prng.uniform(size=n_evt, low=0.0,
high=event_params["exposure_time"])
# Apply dithering
x_offset, y_offset = perform_dither(events["time"], dither_dict)
detx -= x_offset
dety -= y_offset
# PSF scattering of detector coordinates
if instrument_spec["psf"] is not None:
psf_type, psf_spec = instrument_spec["psf"]
if psf_type == "gaussian":
sigma = psf_spec/sigma_to_fwhm/plate_scale_arcsec
detx += prng.normal(loc=0.0, scale=sigma, size=n_evt)
dety += prng.normal(loc=0.0, scale=sigma, size=n_evt)
else:
raise NotImplementedError("PSF type %s not implemented!" % psf_type)
# Convert detector coordinates to chip coordinates.
# Throw out events that don't fall on any chip.
cx = np.trunc(detx)+0.5*np.sign(detx)
cy = np.trunc(dety)+0.5*np.sign(dety)
if event_params["chips"] is None:
events["chip_id"] = np.zeros(n_evt, dtype='int')
keepx = np.logical_and(cx >= -0.5*nx, cx <= 0.5*nx)
keepy = np.logical_and(cy >= -0.5*nx, cy <= 0.5*nx)
keep = np.logical_and(keepx, keepy)
else:
events["chip_id"] = -np.ones(n_evt, dtype='int')
for i, chip in enumerate(event_params["chips"]):
thisc = np.ones(n_evt, dtype='bool')
rtype = chip[0]
args = chip[1:]
r = getattr(rfilter, rtype)(*args)
inside = r.inside(cx, cy)
thisc = np.logical_and(thisc, inside)
events["chip_id"][thisc] = i
keep = events["chip_id"] > -1
mylog.info("%d events were rejected because " % (n_evt-keep.sum()) +
"they do not fall on any CCD.")
n_evt = keep.sum()
if n_evt == 0:
mylog.warning("No events are within the field of view for this source!!!")
else:
# Keep only those events which fall on a chip
for key in events:
events[key] = events[key][keep]
# Convert chip coordinates back to detector coordinates, unless the
# user has specified that they want subpixel resolution
if subpixel_res:
events["detx"] = detx[keep]
events["dety"] = dety[keep]
else:
events["detx"] = cx[keep] + prng.uniform(low=-0.5, high=0.5, size=n_evt)
events["dety"] = cy[keep] + prng.uniform(low=-0.5, high=0.5, size=n_evt)
# Convert detector coordinates back to pixel coordinates by
# adding the dither offsets back in and applying the rotation
# matrix again
det = np.array([events["detx"] + x_offset[keep] - event_params["aimpt_coords"][0],
events["dety"] + y_offset[keep] - event_params["aimpt_coords"][1]])
pix = np.dot(rot_mat.T, det)
events["xpix"] = pix[0,:] + event_params['pix_center'][0]
events["ypix"] = pix[1,:] + event_params['pix_center'][1]
if n_evt > 0:
for key in events:
all_events[key] = np.concatenate([all_events[key], events[key]])
if len(all_events["energy"]) == 0:
mylog.warning("No events from any of the sources in the catalog were detected!")
for key in ["xpix", "ypix", "detx", "dety", "time", "chip_id", event_params["channel_type"]]:
all_events[key] = np.array([])
else:
# Step 4: Scatter energies with RMF
mylog.info("Scattering energies with RMF %s." % os.path.split(rmf.filename)[-1])
all_events = rmf.scatter_energies(all_events, prng=prng)
return all_events, event_params
def __init__(self, ra0, dec0):
self.ra0 = parse_value(ra0, "deg")
self.dec0 = parse_value(dec0, "deg")
self.w = construct_wcs(self.ra0, self.dec0)
def e_to_ch(self, energy):
energy = parse_value(energy, "keV")
return np.searchsorted(self.ebounds_data["E_MIN"], energy)-1