def simulate_spectrum_dataset(model, random_state=0):
edges = np.logspace(-0.5, 1.5, 21) * u.TeV
energy_axis = MapAxis.from_edges(edges, interp="log", name="energy")
aeff = EffectiveAreaTable.from_parametrization(energy=edges).to_region_map()
bkg_model = SkyModel(
spectral_model=PowerLawSpectralModel(
index=2.5, amplitude="1e-12 cm-2 s-1 TeV-1"
),
name="background",
)
bkg_model.spectral_model.amplitude.frozen = True
bkg_model.spectral_model.index.frozen = True
geom = RegionGeom(region=None, axes=[energy_axis])
acceptance = RegionNDMap.from_geom(geom=geom, data=1)
edisp = EDispKernelMap.from_diagonal_response(
energy_axis=energy_axis,
energy_axis_true=energy_axis.copy(name="energy_true"),
geom=geom
)
dataset = SpectrumDatasetOnOff(
aeff=aeff, livetime=100 * u.h, acceptance=acceptance, acceptance_off=5, edisp=edisp
)
dataset.models = bkg_model
bkg_npred = dataset.npred_sig()
dataset.models = model
dataset.fake(random_state=random_state, background_model=bkg_npred)
return dataset
def test_spectrum_dataset_stack_nondiagonal_no_bkg(self):
aeff = EffectiveAreaTable.from_parametrization(self.src.energy.edges,
"HESS")
edisp1 = EDispKernel.from_gauss(self.src.energy.edges,
self.src.energy.edges, 0.1, 0.0)
livetime = self.livetime
dataset1 = SpectrumDataset(counts=None,
livetime=livetime,
aeff=aeff,
edisp=edisp1,
background=None)
livetime2 = livetime
aeff2 = EffectiveAreaTable(self.src.energy.edges[:-1],
self.src.energy.edges[1:], aeff.data.data)
edisp2 = EDispKernel.from_gauss(self.src.energy.edges,
self.src.energy.edges, 0.2, 0.0)
dataset2 = SpectrumDataset(
counts=self.src.copy(),
livetime=livetime2,
aeff=aeff2,
edisp=edisp2,
background=None,
)
dataset1.stack(dataset2)
assert dataset1.counts is None
assert dataset1.background is None
assert dataset1.livetime == 2 * self.livetime
assert_allclose(dataset1.aeff.data.data.to_value("m2"),
aeff.data.data.to_value("m2"))
assert_allclose(dataset1.edisp.get_bias(1 * u.TeV), 0.0, atol=1.2e-3)
assert_allclose(dataset1.edisp.get_resolution(1 * u.TeV),
0.1581,
atol=1e-2)
def test_compute_thresholds_from_parametrization():
energy = np.logspace(-2, 2.0, 100) * u.TeV
aeff = EffectiveAreaTable.from_parametrization(energy=energy)
edisp = EnergyDispersion.from_gauss(e_true=energy,
e_reco=energy,
sigma=0.2,
bias=0)
thresh_lo, thresh_hi = compute_energy_thresholds(
aeff=aeff,
edisp=edisp,
method_lo="area_max",
method_hi="area_max",
area_percent_lo=10,
area_percent_hi=90,
)
assert_allclose(thresh_lo.to("TeV").value, 0.18557, rtol=1e-4)
assert_allclose(thresh_hi.to("TeV").value, 43.818, rtol=1e-4)
thresh_lo, thresh_hi = compute_energy_thresholds(aeff=aeff,
edisp=edisp,
method_hi="area_max",
area_percent_hi=70)
assert_allclose(thresh_hi.to("TeV").value, 100.0, rtol=1e-4)
def test_spectrum_dataset_stack_nondiagonal_no_bkg(spectrum_dataset):
energy = spectrum_dataset.counts.geom.axes[0].edges
aeff = EffectiveAreaTable.from_parametrization(energy, "HESS")
edisp1 = EDispKernel.from_gauss(energy, energy, 0.1, 0)
livetime = 100 * u.s
spectrum_dataset1 = SpectrumDataset(
counts=spectrum_dataset.counts.copy(),
livetime=livetime, aeff=aeff, edisp=edisp1,
)
livetime2 = livetime
aeff2 = EffectiveAreaTable(
energy[:-1], energy[1:], aeff.data.data
)
edisp2 = EDispKernel.from_gauss(energy, energy, 0.2, 0.0)
spectrum_dataset2 = SpectrumDataset(
counts=spectrum_dataset.counts.copy(),
livetime=livetime2,
aeff=aeff2,
edisp=edisp2,
)
spectrum_dataset1.stack(spectrum_dataset2)
assert spectrum_dataset1.background is None
assert spectrum_dataset1.livetime == 2 * livetime
assert_allclose(
spectrum_dataset1.aeff.data.data.to_value("m2"), aeff.data.data.to_value("m2")
)
assert_allclose(spectrum_dataset1.edisp.get_bias(1 * u.TeV), 0.0, atol=1.2e-3)
assert_allclose(spectrum_dataset1.edisp.get_resolution(1 * u.TeV), 0.1581, atol=1e-2)
def test_spectrum_dataset_stack_diagonal_safe_mask(spectrum_dataset):
geom = spectrum_dataset.counts.geom
energy = MapAxis.from_energy_bounds("0.1 TeV", "10 TeV", nbin=30)
energy_true = MapAxis.from_energy_bounds("0.1 TeV",
"10 TeV",
nbin=30,
name="energy_true")
aeff = EffectiveAreaTable.from_parametrization(energy.edges, "HESS")
edisp = EDispKernelMap.from_diagonal_response(energy,
energy_true,
geom=geom.to_image())
livetime = 100 * u.s
background = spectrum_dataset.background
spectrum_dataset1 = SpectrumDataset(
counts=spectrum_dataset.counts.copy(),
livetime=livetime,
aeff=aeff,
edisp=edisp.copy(),
background=background.copy(),
)
livetime2 = 0.5 * livetime
aeff2 = EffectiveAreaTable(energy.edges[:-1], energy.edges[1:],
2 * aeff.data.data)
bkg2 = RegionNDMap.from_geom(geom=geom, data=2 * background.data)
geom = spectrum_dataset.counts.geom
data = np.ones(spectrum_dataset.data_shape, dtype="bool")
data[0] = False
safe_mask2 = RegionNDMap.from_geom(geom=geom, data=data)
spectrum_dataset2 = SpectrumDataset(
counts=spectrum_dataset.counts.copy(),
livetime=livetime2,
aeff=aeff2,
edisp=edisp,
background=bkg2,
mask_safe=safe_mask2,
)
spectrum_dataset1.stack(spectrum_dataset2)
reference = spectrum_dataset.counts.data
assert_allclose(spectrum_dataset1.counts.data[1:], reference[1:] * 2)
assert_allclose(spectrum_dataset1.counts.data[0], 141363)
assert spectrum_dataset1.livetime == 1.5 * livetime
assert_allclose(spectrum_dataset1.background.data[1:],
3 * background.data[1:])
assert_allclose(spectrum_dataset1.background.data[0], background.data[0])
assert_allclose(
spectrum_dataset1.aeff.data.data.to_value("m2"),
4.0 / 3 * aeff.data.data.to_value("m2"),
)
kernel = edisp.get_edisp_kernel()
kernel_stacked = spectrum_dataset1.edisp.get_edisp_kernel()
assert_allclose(kernel_stacked.pdf_matrix[1:], kernel.pdf_matrix[1:])
assert_allclose(kernel_stacked.pdf_matrix[0], 0.5 * kernel.pdf_matrix[0])
def test_from_parametrization():
# Log center of this is 100 GeV
energy = [80, 125] * u.GeV
area_ref = 1.65469579e07 * u.cm ** 2
area = EffectiveAreaTable.from_parametrization(energy, "HESS")
assert_allclose(area.data.data, area_ref)
assert area.data.data.unit == area_ref.unit
# Log center of this is 0.1, 2 TeV
energy = [0.08, 0.125, 32] * u.TeV
area_ref = [1.65469579e07, 1.46451957e09] * u.cm * u.cm
area = EffectiveAreaTable.from_parametrization(energy, "HESS")
assert_allclose(area.data.data, area_ref)
assert area.data.data.unit == area_ref.unit
def get_test_cases():
e_true = Quantity(np.logspace(-1, 2, 120), "TeV")
e_reco = Quantity(np.logspace(-1, 2, 100), "TeV")
return [
dict(model=PowerLawSpectralModel(amplitude="1e2 TeV-1"),
e_true=e_true,
npred=999),
dict(
model=PowerLaw2SpectralModel(amplitude="1",
emin="0.1 TeV",
emax="100 TeV"),
e_true=e_true,
npred=1,
),
dict(
model=PowerLawSpectralModel(amplitude="1e-11 TeV-1 cm-2 s-1"),
aeff=EffectiveAreaTable.from_parametrization(e_true),
livetime="10 h",
npred=1448.05960,
),
dict(
model=PowerLawSpectralModel(reference="1 GeV",
amplitude="1e-11 GeV-1 cm-2 s-1"),
aeff=EffectiveAreaTable.from_parametrization(e_true),
livetime="30 h",
npred=4.34417881,
),
dict(
model=PowerLawSpectralModel(amplitude="1e-11 TeV-1 cm-2 s-1"),
aeff=EffectiveAreaTable.from_parametrization(e_true),
edisp=EnergyDispersion.from_gauss(e_reco=e_reco,
e_true=e_true,
bias=0,
sigma=0.2),
livetime="10 h",
npred=1437.450076,
),
dict(
model=TemplateSpectralModel(
energy=[0.1, 0.2, 0.3, 0.4] * u.TeV,
values=[4.0, 3.0, 1.0, 0.1] * u.Unit("TeV-1"),
),
e_true=[0.1, 0.2, 0.3, 0.4] * u.TeV,
npred=0.554513062,
),
]
def test_spectrum_dataset_stack_nondiagonal_no_bkg(spectrum_dataset):
energy = spectrum_dataset.counts.geom.axes["energy"]
geom = spectrum_dataset.counts.geom.to_image()
edisp1 = EDispKernelMap.from_gauss(
energy_axis=energy,
energy_axis_true=energy.copy(name="energy_true"),
sigma=0.1,
bias=0,
geom=geom)
edisp1.exposure_map.data += 1
aeff = EffectiveAreaTable.from_parametrization(
energy.edges, "HESS").to_region_map(geom.region)
geom = spectrum_dataset.counts.geom
counts = RegionNDMap.from_geom(geom=geom)
gti = GTI.create(start=0 * u.s, stop=100 * u.s)
spectrum_dataset1 = SpectrumDataset(
counts=counts,
exposure=aeff * gti.time_sum,
edisp=edisp1,
meta_table=Table({"OBS_ID": [0]}),
gti=gti.copy(),
)
edisp2 = EDispKernelMap.from_gauss(
energy_axis=energy,
energy_axis_true=energy.copy(name="energy_true"),
sigma=0.2,
bias=0.0,
geom=geom)
edisp2.exposure_map.data += 1
gti2 = GTI.create(start=100 * u.s, stop=200 * u.s)
spectrum_dataset2 = SpectrumDataset(
counts=counts,
exposure=aeff * gti2.time_sum,
edisp=edisp2,
meta_table=Table({"OBS_ID": [1]}),
gti=gti2,
)
spectrum_dataset1.stack(spectrum_dataset2)
assert_allclose(spectrum_dataset1.meta_table["OBS_ID"][0], [0, 1])
assert spectrum_dataset1.background_model is None
assert_allclose(spectrum_dataset1.gti.time_sum.to_value("s"), 200)
assert_allclose(spectrum_dataset1.exposure.quantity[2].to_value("m2 s"),
1573851.079861)
kernel = edisp1.get_edisp_kernel()
assert_allclose(kernel.get_bias(1 * u.TeV), 0.0, atol=1.2e-3)
assert_allclose(kernel.get_resolution(1 * u.TeV), 0.1581, atol=1e-2)
def test_set_model(self):
aeff = EffectiveAreaTable.from_parametrization(self.src.energy.edges,
"HESS")
edisp = EnergyDispersion.from_diagonal_response(
self.src.energy.edges, self.src.energy.edges)
dataset = SpectrumDataset(None, self.src, self.livetime, None, aeff,
edisp, self.bkg)
with pytest.raises(AttributeError):
dataset.parameters
dataset.model = self.source_model
assert dataset.parameters[0] == self.source_model.parameters[0]
def test_compute_thresholds_from_parametrization():
energy = np.logspace(-2, 2.0, 100) * u.TeV
aeff = EffectiveAreaTable.from_parametrization(energy=energy)
thresh_lo = aeff.find_energy(aeff=0.1 * aeff.max_area)
e_max = aeff.energy.edges[-1]
thresh_hi = aeff.find_energy(
aeff=0.9 * aeff.max_area, energy_min=0.1 * e_max, energy_max=e_max
)
assert_allclose(thresh_lo.to("TeV").value, 0.18557, rtol=1e-4)
assert_allclose(thresh_hi.to("TeV").value, 43.818, rtol=1e-4)
def test_spectrum_dataset_stack_diagonal_safe_mask(spectrum_dataset):
geom = spectrum_dataset.counts.geom
energy = np.logspace(-1, 1, 31) * u.TeV
aeff = EffectiveAreaTable.from_parametrization(energy, "HESS")
edisp = EDispKernel.from_diagonal_response(energy, energy)
livetime = 100 * u.s
background = spectrum_dataset.background
spectrum_dataset1 = SpectrumDataset(
counts=spectrum_dataset.counts.copy(),
livetime=livetime,
aeff=aeff,
edisp=edisp,
background=background.copy(),
)
livetime2 = 0.5 * livetime
aeff2 = EffectiveAreaTable(energy[:-1], energy[1:], 2 * aeff.data.data)
bkg2 = RegionNDMap.from_geom(geom=geom, data=2 * background.data)
geom = spectrum_dataset.counts.geom
data = np.ones(spectrum_dataset.data_shape, dtype="bool")
data[0] = False
safe_mask2 = RegionNDMap.from_geom(geom=geom, data=data)
spectrum_dataset2 = SpectrumDataset(
counts=spectrum_dataset.counts.copy(),
livetime=livetime2,
aeff=aeff2,
edisp=edisp,
background=bkg2,
mask_safe=safe_mask2,
)
spectrum_dataset1.stack(spectrum_dataset2)
reference = spectrum_dataset.counts.data
assert_allclose(spectrum_dataset1.counts.data[1:], reference[1:] * 2)
assert_allclose(spectrum_dataset1.counts.data[0], 141363)
assert spectrum_dataset1.livetime == 1.5 * livetime
assert_allclose(spectrum_dataset1.background.data[1:],
3 * background.data[1:])
assert_allclose(spectrum_dataset1.background.data[0], background.data[0])
assert_allclose(
spectrum_dataset1.aeff.data.data.to_value("m2"),
4.0 / 3 * aeff.data.data.to_value("m2"),
)
assert_allclose(spectrum_dataset1.edisp.pdf_matrix[1:],
edisp.pdf_matrix[1:])
assert_allclose(spectrum_dataset1.edisp.pdf_matrix[0],
0.5 * edisp.pdf_matrix[0])
def simulate_spectrum_dataset(model, random_state=0):
energy = np.logspace(-0.5, 1.5, 21) * u.TeV
aeff = EffectiveAreaTable.from_parametrization(energy=energy)
bkg_model = PowerLawSpectralModel(index=2.5, amplitude="1e-12 cm-2 s-1 TeV-1")
dataset = SpectrumDatasetOnOff(
aeff=aeff, model=model, livetime=100 * u.h, acceptance=1, acceptance_off=5
)
eval = SpectrumEvaluator(model=bkg_model, aeff=aeff, livetime=100 * u.h)
bkg_model = eval.compute_npred()
dataset.fake(random_state=random_state, background_model=bkg_model)
return dataset
def test_set_model(self):
aeff = EffectiveAreaTable.from_parametrization(self.src.energy.edges,
"HESS")
edisp = EDispKernel.from_diagonal_response(self.src.energy.edges,
self.src.energy.edges)
dataset = SpectrumDataset(None, self.src, self.livetime, None, aeff,
edisp, self.bkg)
spectral_model = PowerLawSpectralModel()
model = SkyModel(spectral_model=spectral_model, name="test")
dataset.models = model
assert dataset.models["test"] is model
models = Models([model])
dataset.models = models
assert dataset.models["test"] is model
def test_spectrum_dataset_stack_diagonal_safe_mask(self):
aeff = EffectiveAreaTable.from_parametrization(self.src.energy.edges,
"HESS")
edisp = EDispKernel.from_diagonal_response(self.src.energy.edges,
self.src.energy.edges)
livetime = self.livetime
dataset1 = SpectrumDataset(
counts=self.src.copy(),
livetime=livetime,
aeff=aeff,
edisp=edisp,
background=self.bkg.copy(),
)
livetime2 = 0.5 * livetime
aeff2 = EffectiveAreaTable(self.src.energy.edges[:-1],
self.src.energy.edges[1:],
2 * aeff.data.data)
bkg2 = CountsSpectrum(
self.src.energy.edges[:-1],
self.src.energy.edges[1:],
data=2 * self.bkg.data,
)
safe_mask2 = np.ones_like(self.src.data, bool)
safe_mask2[0] = False
dataset2 = SpectrumDataset(
counts=self.src.copy(),
livetime=livetime2,
aeff=aeff2,
edisp=edisp,
background=bkg2,
mask_safe=safe_mask2,
)
dataset1.stack(dataset2)
assert_allclose(dataset1.counts.data[1:], self.src.data[1:] * 2)
assert_allclose(dataset1.counts.data[0], self.src.data[0])
assert dataset1.livetime == 1.5 * self.livetime
assert_allclose(dataset1.background.data[1:], 3 * self.bkg.data[1:])
assert_allclose(dataset1.background.data[0], self.bkg.data[0])
assert_allclose(
dataset1.aeff.data.data.to_value("m2"),
4.0 / 3 * aeff.data.data.to_value("m2"),
)
assert_allclose(dataset1.edisp.pdf_matrix[1:], edisp.pdf_matrix[1:])
assert_allclose(dataset1.edisp.pdf_matrix[0],
0.5 * edisp.pdf_matrix[0])
def test_spectrum_dataset_stack_nondiagonal_no_bkg(spectrum_dataset):
energy = spectrum_dataset.counts.geom.axes[0]
geom = spectrum_dataset.counts.geom.to_image()
edisp1 = EDispKernelMap.from_gauss(energy, energy, 0.1, 0, geom=geom)
edisp1.exposure_map.data += 1
aeff = EffectiveAreaTable.from_parametrization(
energy.edges, "HESS").to_region_map(geom.region)
livetime = 100 * u.s
spectrum_dataset1 = SpectrumDataset(counts=spectrum_dataset.counts.copy(),
livetime=livetime,
aeff=aeff,
edisp=edisp1,
meta_table=Table({"OBS_ID": [0]}))
livetime2 = livetime
aeff2 = aeff.copy()
edisp2 = EDispKernelMap.from_gauss(energy, energy, 0.2, 0.0, geom=geom)
edisp2.exposure_map.data += 1
spectrum_dataset2 = SpectrumDataset(counts=spectrum_dataset.counts.copy(),
livetime=livetime2,
aeff=aeff2,
edisp=edisp2,
meta_table=Table({"OBS_ID": [1]}))
spectrum_dataset1.stack(spectrum_dataset2)
assert_allclose(spectrum_dataset1.meta_table["OBS_ID"][0], [0, 1])
assert spectrum_dataset1.background is None
assert spectrum_dataset1.livetime == 2 * livetime
assert_allclose(spectrum_dataset1.aeff.quantity.to_value("m2"),
aeff.quantity.to_value("m2"))
kernel = edisp1.get_edisp_kernel()
assert_allclose(kernel.get_bias(1 * u.TeV), 0.0, atol=1.2e-3)
assert_allclose(kernel.get_resolution(1 * u.TeV), 0.1581, atol=1e-2)
def test_spectrum_dataset_stack_diagonal_safe_mask(spectrum_dataset):
geom = spectrum_dataset.counts.geom
energy = MapAxis.from_energy_bounds("0.1 TeV", "10 TeV", nbin=30)
energy_true = MapAxis.from_energy_bounds("0.1 TeV",
"10 TeV",
nbin=30,
name="energy_true")
aeff = EffectiveAreaTable.from_parametrization(
energy.edges, "HESS").to_region_map(geom.region)
livetime = 100 * u.s
gti = GTI.create(start=0 * u.s, stop=livetime)
exposure = aeff * livetime
edisp = EDispKernelMap.from_diagonal_response(energy,
energy_true,
geom=geom.to_image())
edisp.exposure_map.data = exposure.data[:, :, np.newaxis, :]
background = spectrum_dataset.background_model.map.copy()
spectrum_dataset1 = SpectrumDataset(name="ds1",
counts=spectrum_dataset.counts.copy(),
exposure=exposure.copy(),
edisp=edisp.copy(),
models=BackgroundModel(
background,
name="ds1-bkg",
datasets_names=["ds1"]),
gti=gti.copy())
livetime2 = 0.5 * livetime
gti2 = GTI.create(start=200 * u.s, stop=200 * u.s + livetime2)
aeff2 = aeff * 2
bkg2 = RegionNDMap.from_geom(geom=geom, data=2 * background.data)
geom = spectrum_dataset.counts.geom
data = np.ones(spectrum_dataset.data_shape, dtype="bool")
data[0] = False
safe_mask2 = RegionNDMap.from_geom(geom=geom, data=data)
exposure2 = aeff2 * livetime2
edisp = edisp.copy()
edisp.exposure_map.data = exposure2.data[:, :, np.newaxis, :]
spectrum_dataset2 = SpectrumDataset(name="ds2",
counts=spectrum_dataset.counts.copy(),
exposure=exposure2,
edisp=edisp,
models=BackgroundModel(
bkg2,
name="ds2-bkg",
datasets_names=["ds2"]),
mask_safe=safe_mask2,
gti=gti2)
spectrum_dataset1.stack(spectrum_dataset2)
reference = spectrum_dataset.counts.data
assert_allclose(spectrum_dataset1.counts.data[1:], reference[1:] * 2)
assert_allclose(spectrum_dataset1.counts.data[0], 141363)
assert_allclose(spectrum_dataset1.exposure.data[0], 4.755644e+09)
assert_allclose(spectrum_dataset1.background_model.map.data[1:],
3 * background.data[1:])
assert_allclose(spectrum_dataset1.background_model.map.data[0],
background.data[0])
assert_allclose(
spectrum_dataset1.exposure.quantity.to_value("m2s"),
2 * (aeff * livetime).quantity.to_value("m2s"),
)
kernel = edisp.get_edisp_kernel()
kernel_stacked = spectrum_dataset1.edisp.get_edisp_kernel()
assert_allclose(kernel_stacked.pdf_matrix[1:], kernel.pdf_matrix[1:])
assert_allclose(kernel_stacked.pdf_matrix[0], 0.5 * kernel.pdf_matrix[0])
import numpy as np
import matplotlib.pyplot as plt
import astropy.units as u
from gammapy.irf import EffectiveAreaTable
energy = np.logspace(-3, 3, 100) * u.TeV
for instrument in ['HESS', 'HESS2', 'CTA']:
aeff = EffectiveAreaTable.from_parametrization(energy, instrument)
ax = aeff.plot(label=instrument)
ax.set_yscale('log')
ax.set_xlim([1e-3, 1e3])
ax.set_ylim([1e3, 1e12])
plt.legend(loc='best')
plt.show()
from gammapy.spectrum.models import PowerLaw
# ## Create detector
#
# For the sake of self consistency of this tutorial, we will simulate a simple detector. For a real application you would want to replace this part of the code with loading the IRFs or your detector.
# In[ ]:
e_true = np.logspace(-2, 2.5, 109) * u.TeV
e_reco = np.logspace(-2, 2, 79) * u.TeV
edisp = EnergyDispersion.from_gauss(e_true=e_true,
e_reco=e_reco,
sigma=0.2,
bias=0)
aeff = EffectiveAreaTable.from_parametrization(energy=e_true)
fig, axes = plt.subplots(1, 2, figsize=(12, 6))
edisp.plot_matrix(ax=axes[0])
aeff.plot(ax=axes[1])
# ## Power law
#
# In this section we will simulate one observation using a power law model.
# In[ ]:
pwl = PowerLaw(index=2.3,
amplitude=1e-11 * u.Unit("cm-2 s-1 TeV-1"),
reference=1 * u.TeV)
print(pwl)
