From 1579688fa4ccecc126cbd633bd6d5d113191680b Mon Sep 17 00:00:00 2001 From: gschwefer Date: Mon, 24 Jun 2024 16:47:20 +0200 Subject: [PATCH 1/2] Add Gamera spectral model example --- recipes/fitting-with-gamera/env.yml | 14 + .../fitting_with_gamera.ipynb | 322 ++++++ .../fitting-with-gamera/radiation_field.txt | 1001 +++++++++++++++++ 3 files changed, 1337 insertions(+) create mode 100644 recipes/fitting-with-gamera/env.yml create mode 100644 recipes/fitting-with-gamera/fitting_with_gamera.ipynb create mode 100644 recipes/fitting-with-gamera/radiation_field.txt diff --git a/recipes/fitting-with-gamera/env.yml b/recipes/fitting-with-gamera/env.yml new file mode 100644 index 0000000..4838ef6 --- /dev/null +++ b/recipes/fitting-with-gamera/env.yml @@ -0,0 +1,14 @@ +# Declare your specific environment +#Gamera is not pip installable therefore it is not listed here + +name: gp-gamera-fit + +channels: + - conda-forge + +dependencies: + - gammapy=1.2 + - python=3.9 + - numpy=1.24 + - jupyter + - matplotlib diff --git a/recipes/fitting-with-gamera/fitting_with_gamera.ipynb b/recipes/fitting-with-gamera/fitting_with_gamera.ipynb new file mode 100644 index 0000000..5915587 --- /dev/null +++ b/recipes/fitting-with-gamera/fitting_with_gamera.ipynb @@ -0,0 +1,322 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Fitting a physical model using Gamera\n", + "\n", + "## Context\n", + "\n", + "[Gamera](http://libgamera.github.io/GAMERA/docs/documentation.html) is a source modelling code for gamma ray astronomy that allows for the calculation of gamma-ray spectra from underlying populations of leptonic and hadronic cosmic rays. Fitting the resulting spectra to data would directly allow to constrain the parameters of these underlying distributions.\n", + "\n", + "## Proposed approach\n", + "\n", + "\n", + "Here, we will demonstrate the two possible ways in which Gamera can be used in combination with gammapy to fit the spectra of gamma-ray sources. As an example, we will use the scenario of a leptonic source producing gamma rays through Inverse Compton scattering.\n", + "\n", + "The two possible approaches are\n", + " \n", + "* Subclassing `~gammapy.modeling.models.SpectralModel` and creating a `GameraSpectralModel`. This is probbaly the most elegant way to combine Gamera and gammapy, but can also be slow because it requires the repeated execution of Gamera for every model evaluation\n", + "* Creating a `~gammapy.modeling.models.TemplateNDSpectralModel` from Gamera spectra produced on a grid of model parameters. While less elegant than the first approach, it can be significantly faster because no Gamera evaluations are required during the fit.\n", + "\n", + "For more modelling options with Gamera, see the [documentation](http://libgamera.github.io/GAMERA/docs/documentation.html).\n", + "Also note that gamera is not pip installable. See installation instructions [here](http://libgamera.github.io/GAMERA/docs/download_installation.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Setup\n", + "\n", + "As always, we start the notebook with some setup and imports. The environment variable `GAMERA_LIB_PATH` should point to the direcotry containing the installed Gamera library." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import sys\n", + "import os\n", + "sys.path.append(os.environ[\"GAMERA_LIB_PATH\"])\n", + "import gappa as gp" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import astropy.units as u\n", + "from astropy.coordinates import SkyCoord,Angle\n", + "import itertools\n", + "from regions import CircleSkyRegion" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from gammapy.maps import MapAxis,RegionNDMap,RegionGeom\n", + "from gammapy.modeling.models import (\n", + " SpectralModel,\n", + " SPECTRAL_MODEL_REGISTRY,\n", + " TemplateNDSpectralModel\n", + ")\n", + "from gammapy.modeling import Parameter " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Approach 1: GameraSpectralModel\n", + "\n", + "Below is the implementation of the `GameraSpectralModel` class. It is a subclass of `SpectralModel`. With every evaluation, it evolves a population of electrons in a time-independent environment (i.e. fixed magnetic field and radiation field), takes the output electron spectrum and calculates the gamma-ray spectrum from this.\n", + "\n", + "As the radiation field, we use the model from [Popescu et al. 2017](https://doi.org/10.1093/mnras/stx1282) together with the CMB spectrum, in this case evaluated at the position of the crab nebula. Any other model or radiation spectrum is also possible. It is read here from a txt file with the energies and energy densities of the radiation.\n", + "\n", + "The model has a number of parameters related to the modelled source. Many of these should not be fit, but just be set at the model instantiation and frozen. \n", + "\n", + "Also, Gamera does not work with astropy units. Therefore, the input quantities to the `GameraSpectralModel` need to be internally stripped of their units for the Gamera calculations. The units are then reattached to the output.\n", + "\n", + "For more details about the Gamera code and methods, see [here](http://libgamera.github.io/GAMERA/docs/time_independent_modeling.html).\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "class GameraSpectralModel(SpectralModel):\n", + " \"\"\"Spectral model from GAMERA synchrotron and IC emission.\n", + " A power law with cutoff is assumed for the electron spectrum.\n", + " To limit the span of the parameters space, we fit the log10 of the parameters\n", + " whose range is expected to cover several orders of magnitudes.\n", + "\n", + " Some of the parameters (like the distance) should not be fit, but are there just to evaluate the model.\n", + " \"\"\"\n", + "\n", + " tag = [\"GAMERA\", \"g\"]\n", + " # parameters that we actually might want to fit\n", + " index = Parameter(\"index\", 2.5, min=1.5, max=4.0) #it's positive: E^-index\n", + " log10_effic = Parameter(\"log10_effic\", -2, min=-8, max=0)\n", + " log10_E_min = Parameter(\"log10_E_min\", -5, min=-9, max=0,frozen=True) # in TeV\n", + " log10_E_cut = Parameter(\"log10_E_cut\", 4, min=0, max=6,frozen=True) # in TeV\n", + " log10_B = Parameter(\"log10_B\", -5, min=-8, max=-2,frozen=True) #in Gauss\n", + "\n", + " # parameters that we should not fit but just provide\n", + " L_tot = Parameter(\"L_tot\", \"1e43 erg s-1\", min=1e30, max=1e50, frozen=True) # in ergs/s\n", + " d = Parameter(\"d\", \"2 kpc\", min=1, max=10, frozen=True) # in kpc\n", + " age = Parameter(\"age\", \"3e4 yr\", min=1e3, max=1e6, frozen=True)\n", + "\n", + "\n", + " @staticmethod\n", + " def evaluate(\n", + " energy,\n", + " log10_B,\n", + " index,\n", + " log10_effic,\n", + " log10_E_min,\n", + " log10_E_cut,\n", + " L_tot,\n", + " d,\n", + " age,\n", + " ):\n", + " # conversions\n", + " B = (10 ** log10_B) * u.G\n", + " effic = 10 ** log10_effic\n", + " E_min = (10 ** log10_E_min) * u.TeV\n", + " E_cut = (10 ** log10_E_cut) * u.TeV\n", + "\n", + " # Get the relevant GAMERA modules\n", + " fu = gp.Utils()\n", + " fp = gp.Particles()\n", + " fr = gp.Radiation()\n", + " fp.ToggleQuietMode()\n", + " fp.SetSolverMethod(1)\n", + " fr.ToggleQuietMode()\n", + "\n", + " # GAMERA doesn't know about astropy units\n", + " # so we need to get everything in the right unit\n", + " # and as a normal float and not a quantity\n", + " b_field = B.to_value('G')\n", + " t_max = age.to_value('yr')\n", + " distance = d.to_value('pc')\n", + " e_cut = np.log10(E_cut.to_value('erg'))\n", + " e_min = np.log10(E_min.to_value('erg'))\n", + " norm = (effic * L_tot).to_value('erg s-1')\n", + " energy_shape=energy.shape\n", + " photon_energies = energy.flatten().to_value('erg')\n", + " index = index.value\n", + " # Define the electron energy range and the injected spectrum\n", + " # We want to go beyond the cutoff so we use two orders of magnitude more than e_cut\n", + " energy_electrons_edges = np.logspace(e_min, e_cut+2, 100+1) # it's in ergs\n", + "\n", + " padded = False\n", + "\n", + " \n", + " # GAMERA removes the highest and lowest energy bin so we need to pad it so that our choice of E_min is the true one\n", + " step_log = np.diff(np.log10(energy_electrons_edges))[0]\n", + " energy_electrons_edges = np.append(energy_electrons_edges[0]*10**-step_log, energy_electrons_edges)\n", + " energy_electrons_edges = np.append(energy_electrons_edges, energy_electrons_edges[-1]*10**step_log)\n", + " padded = True\n", + "\n", + " if padded:\n", + " range = slice(1,-1, 1)\n", + " else:\n", + " range = slice(None, None, 1)\n", + "\n", + " energy_electrons = MapAxis.from_edges(energy_electrons_edges, interp='log', unit='erg')\n", + " exp_cutoff = np.exp(-(energy_electrons.center.to('erg')/E_cut.to('erg')).value)\n", + " power_law = (energy_electrons.center.to_value('erg') ** -index)*exp_cutoff\n", + "\n", + " # Normalize to total power\n", + " # Note that if we have padded, the range is different\n", + " power_law *= norm / fu.Integrate(list(zip(energy_electrons.center.to_value('erg')[range], power_law[range] * energy_electrons.center.to_value('erg')[range])))\n", + "\n", + " # Bundle together in the way GAMERA wants\n", + " power_law_spectrum = np.array(list(zip(energy_electrons.center.to_value('erg'), power_law)))\n", + "\n", + " #Read the radiation field spectrum, in this case the Popescu et al. 2017 model + CM at the crab nebula position. \n", + " rad_field = np.loadtxt(\"radiation_field.txt\")\n", + "\n", + " RADIATION_FIELD = list(zip(rad_field[:,0], rad_field[:,1]))\n", + "\n", + " # Set everything that is left\n", + " fp.AddArbitraryTargetPhotons(RADIATION_FIELD)\n", + " fp.SetCustomInjectionSpectrum(power_law_spectrum) # the injection rate is constant and given by the normalization of injected PL\n", + " fr.AddArbitraryTargetPhotons(RADIATION_FIELD)\n", + " fr.SetDistance(distance)\n", + " fp.SetBField(b_field)\n", + " fr.SetBField(b_field)\n", + "\n", + "\n", + " #Run the evolution of the electron spectrum and set the output as parent population for radiation calculation\n", + " fp.SetAge(t_max)\n", + " fp.CalculateElectronSpectrum()\n", + " sp = np.array(fp.GetParticleSpectrum())\n", + " fr.SetElectrons(sp)\n", + "\n", + " # compute the gamma-ray spectrum on the points given by the data\n", + " fr.CalculateDifferentialPhotonSpectrum(photon_energies)\n", + " rad = np.array(fr.GetTotalSpectrum()) # this is (dN/dE vs E, units: 1/ erg / cm^2 / s vs TeV)\n", + "\n", + " sed=rad[:,1]\n", + "\n", + " # Get back to the world of units\n", + " sed *= u.erg**-1 * u.cm**-2 *u.s **-1\n", + "\n", + " return sed.to(\"1 / (cm2 eV s)\").reshape(energy_shape)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "SPECTRAL_MODEL_REGISTRY.append(GameraSpectralModel)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "gamera_custom_spectral_model=GameraSpectralModel()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Approach 2: TemplateNDSpectralModel\n", + "\n", + "The other option is to fill a grid of spectra dependent on the parameters to be fit. Here, we demonstrate this using the `GameraSpectralModel` to fill the grid of spectra, with `log10_effic` and `index` as the parameters to be fit. Of course, any other function that returns the spectrum as the function of the parameters to be fit could be used.\n", + "\n", + "As an example we use the crab nebula position as the center of the `CircleSkyRegion` on which the model is based." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def make_template_spectral_model(spectral_model,on_region,n_energies,n_efficiencies,n_index,log10_energy_bounds,log10_eff_bounds,index_bounds):\n", + "\n", + " energy_axis=MapAxis.from_energy_edges(np.logspace(log10_energy_bounds[0],log10_energy_bounds[1],n_energies+1)*u.TeV,name=\"energy_true\")\n", + " efficiency_axis=MapAxis(np.linspace(log10_eff_bounds[0],log10_eff_bounds[1],n_efficiencies+1),name=\"log10_effic\",node_type=\"edges\")\n", + " spectral_index_axis=MapAxis(np.linspace(index_bounds[0],index_bounds[1],n_index+1),name=\"index\",node_type=\"edges\")\n", + "\n", + " region_geom=RegionGeom(on_region,axes=[energy_axis,efficiency_axis,spectral_index_axis])\n", + "\n", + " template_map=np.empty((n_efficiencies,n_index,n_energies))\n", + "\n", + " for (i, j) in itertools.product(range(n_efficiencies),range(n_index)):\n", + " spectral_model.parameters[\"log10_effic\"].value=efficiency_axis.center[i]\n", + " spectral_model.parameters[\"index\"].value=spectral_index_axis.center[j]\n", + " template_map[j,i]=spectral_model(energy_axis.center)\n", + "\n", + " template_region_map=RegionNDMap(region_geom,data=template_map,unit=u.eV**-1*u.cm**-2*u.s**-1)\n", + "\n", + " template_spectral_model=TemplateNDSpectralModel(template_region_map)\n", + "\n", + " return template_spectral_model\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "target_position = SkyCoord(ra=83.63, dec=22.01, unit=\"deg\", frame=\"icrs\")\n", + "on_region_radius = Angle(\"0.11 deg\")\n", + "on_region = CircleSkyRegion(center=target_position, radius=on_region_radius)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "gamera_template_spectral_model=make_template_spectral_model(gamera_custom_spectral_model,on_region,30,10,10,(-1,2),(-2.5,0),(1.5,4))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/recipes/fitting-with-gamera/radiation_field.txt b/recipes/fitting-with-gamera/radiation_field.txt new file mode 100644 index 0000000..126e873 --- /dev/null +++ b/recipes/fitting-with-gamera/radiation_field.txt @@ -0,0 +1,1001 @@ 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+7.918256013601204737e-12 4.308546820944221020e+08 +8.229536287773481307e-12 3.891269394722682834e+08 +8.553053525353146150e-12 3.524176150706924796e+08 +8.889288782436129222e-12 3.193676518194457293e+08 +9.238742026261571834e-12 2.975444851153430939e+08 +9.601932878641415164e-12 2.828971647755373120e+08 +9.979401388615488257e-12 2.684161715911573768e+08 +1.037170883548100740e-11 2.507889923801468313e+08 +1.077943856339052853e-11 2.343209924370757639e+08 +1.120319684875940312e-11 2.189357706357576549e+08 +1.164361380177249142e-11 2.045540722271288931e+08 +1.210134430333068259e-11 1.905902491575818956e+08 +1.257706897883037177e-11 1.747255934536984563e+08 +1.307149521022389607e-11 1.601630343815174401e+08 +1.358535818786580886e-11 1.486100300182091594e+08 +1.411942200370903705e-11 1.387881189312339425e+08 +1.467448078747646730e-11 1.292618407063990980e+08 +1.525135988749738365e-11 1.088302654823811352e+08 +1.585091709796463326e-11 9.064068939191827178e+07 +1.647404393443735833e-11 7.549204911038434505e+07 +1.712166695948597392e-11 6.287588047430668026e+07 +1.779474916045048737e-11 5.236873721698416770e+07 +1.849429138136091424e-11 4.361798832268333435e+07 +1.922133381114890531e-11 3.632997095612666756e+07 +1.997695753036357714e-11 3.026012828012827411e+07 +2.076228611869136990e-11 2.520479727645695582e+07 From 7867e938fd6e5f78fb58b8ea59f3ca1854079c83 Mon Sep 17 00:00:00 2001 From: gschwefer Date: Mon, 24 Jun 2024 18:15:09 +0200 Subject: [PATCH 2/2] Add link to radiation model --- recipes/fitting-with-gamera/fitting_with_gamera.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/recipes/fitting-with-gamera/fitting_with_gamera.ipynb b/recipes/fitting-with-gamera/fitting_with_gamera.ipynb index 5915587..7eaada8 100644 --- a/recipes/fitting-with-gamera/fitting_with_gamera.ipynb +++ b/recipes/fitting-with-gamera/fitting_with_gamera.ipynb @@ -81,7 +81,7 @@ "\n", "Below is the implementation of the `GameraSpectralModel` class. It is a subclass of `SpectralModel`. With every evaluation, it evolves a population of electrons in a time-independent environment (i.e. fixed magnetic field and radiation field), takes the output electron spectrum and calculates the gamma-ray spectrum from this.\n", "\n", - "As the radiation field, we use the model from [Popescu et al. 2017](https://doi.org/10.1093/mnras/stx1282) together with the CMB spectrum, in this case evaluated at the position of the crab nebula. Any other model or radiation spectrum is also possible. It is read here from a txt file with the energies and energy densities of the radiation.\n", + "As the radiation field, we use the model from [Popescu et al. 2017](https://doi.org/10.1093/mnras/stx1282) together with the CMB spectrum, in this case evaluated at the position of the crab nebula. The data of the model can also be found [here](http://cdsarc.u-strasbg.fr/viz-bin/Cat?J/MNRAS/470/2539#/browse). Any other model or radiation spectrum is also possible. It is read here from a txt file with the energies and energy densities of the radiation.\n", "\n", "The model has a number of parameters related to the modelled source. Many of these should not be fit, but just be set at the model instantiation and frozen. \n", "\n",