Advanced documentation

The “advanced documentation” is the almost complete documentation of all modules.

prince_cr.config – default configuration options

The module contains all static options of PriNCe that are not meant to be changed in run time.

PriNCe configuration module.

prince_cr.config.E_CMB = 2.34823e-13

CMB energy kB*T0 [GeV]

prince_cr.config.H_0 = 70.5

Hubble constant

prince_cr.config.Omega_Lambda = 0.73

Omega_Lambda

prince_cr.config.Omega_m = 0.27

Omega_m

prince_cr.config.cosmic_ray_grid = (3, 14, 8)

Cosmic ray energy grid (defines system size for solver) Number of bins in multiples of 4 recommended for maximal vectorization efficiency for 256 bit AVX or similar Format (log10(E_min), log10(E_max), nbins/decade of energy)

prince_cr.config.data_dir = '/home/docs/checkouts/readthedocs.org/user_builds/prince/checkouts/latest/prince_cr/data'

Directory where the data files for the calculation are stored

prince_cr.config.db_fname = 'prince_db_05.h5'

PrinceDB file name

prince_cr.config.debug_level = 1

Debug flag for verbose printing, 0 silences PriNCe entirely

prince_cr.config.grid_scale = 'E'

Scale of the energy grid ‘E’: logarithmic in energy E_i = E_min * (Delta)^i ‘logE’: linear grid in x = log_10(E): x_i = x_min + i * Delta

prince_cr.config.override_debug_fcn = []

Printout debug info only for functions in this list (just give the name, “get_solution” for instance) Warning, this option slows down initialization by a lot. Use only when needed.

prince_cr.config.override_max_level = 10

Override debug printout for debug levels < value for the functions above

prince_cr.config.pf = 'Linux-5.19.0-1028-aws-x86_64-with-debian-buster-sid'

determine shared library extension and MKL path

prince_cr.config.photon_grid = (-15, -6, 8)

Photon grid of target field, only for calculation of rates

prince_cr.config.print_module = False

Print module name in debug output

prince_cr.config.redist_fname = 'sophia_redistribution_logbins.npy'

Model file for redistribution functions (from SOPHIA or similar)

prince_cr.config.redist_threshold_ID = 101

Particle ID for which redistribution functions are needed to be taken into account. The default value is 101 (proton). All particles with smaller IDs, i.e. neutrinos, pions, muons etc., will have energy redistributions. For larger IDs (nuclei) the boost conservation is employed.

prince_cr.config.semi_lagr_method = '5th_order'

Order of semi-lagrangian for energy derivative

prince_cr.config.tau_dec_threshold = inf

Threshold lifetime value for explicit transport of particles of this type. It means that if a particle is unstable with lifetime smaller than this threshold, it will be decayed until all final state particles of this chain are stable. In other words: short intermediate states will be integrated out

prince_cr.config.x_cut = 0.0001

Cut on energy redistribution functions Resitribution below this x value are set to 0. “x_cut” : 0., “x_cut_proton” : 0.,

prince_cr.config.y_cut = inf

cut on photon energy, cross section above y = E_cr e_ph / m_cr does not contribute

prince_cr.core – Core module

This module contains the main program features. Instantiating prince_cr.core.PriNCeRun will initialize the data structures and particle tables, create and fill the interaction and decay matrix and check if all information for the calculation of inclusive fluxes in the atmosphere is available.

Provides user interface and runtime management.

class prince_cr.core.PriNCeRun(*args, **kwargs)[source]

This is a draft of the main class.

This class is supposed to interprete the config options and initialize all necessary stuff in order. This class is meant to keep all separate ingredients together in one place, and it is inteded to be passed to further classes via self.

prince_cr.data – (particle) Species management

The prince_cr.data.SpeciesManager handles the bookkeeping of :class:`prince_cr.data.PrinceSpecies`s.

Module inteded to contain some prince-specific data structures.

class prince_cr.data.EnergyGrid(lower, upper, bins_dec)[source]

Class for constructing a grid for discrete distributions.

Since we discretize everything in energy, the name seems appropriate. All grids are log spaced.

Parameters:
  • lower (float) – log10 of low edge of the lowest bin
  • upper (float) – log10 of upper edge of the highest bin
  • bins_dec (int) – bins per decade of energy
class prince_cr.data.PrinceDB[source]

Provides access to data stored in an HDF5 file.

The file contains all tables for runnin PriNCe. Currently the only still required file is the particle database. The tools to generate this database are publicly available in PriNCe-data-utils.

class prince_cr.data.PrinceSpecies(ncoid, princeidx, d)[source]

Bundles different particle properties for simplified availability of particle properties in prince_cr.core.PriNCeRun.

Parameters:
  • pdgid (int) – PDG ID of the particle
  • particle_db (object) – a dictionary with particle properties
  • d (int) – dimension of the energy grid
static calc_AZN(nco_id)[source]

Returns mass number A, charge Z and neutron number N of nco_id.

indices(grid_tag='default')[source]

Returns a list of all indices in the state vector.

Returns:array of indices in state vector PrinceRun.phi
Return type:(numpy.array)
lbin(grid_tag='default')[source]

Returns lower bin of particle range in state vector.

Returns:lower bin in state vector PrinceRun.phi
Return type:(int)
lidx(grid_tag='default')[source]

Returns lower index of particle range in state vector.

Returns:lower index in state vector PrinceRun.phi
Return type:(int)
ubin(grid_tag='default')[source]

Returns upper bin of particle range in state vector.

Returns:upper bin in state vector PrinceRun.phi
Return type:(int)
uidx(grid_tag='default')[source]

Returns upper index of particle range in state vector.

Returns:upper index in state vector PrinceRun.phi
Return type:(int)
A = None

Mass, charge, neutron number

N = None

Mass, charge, neutron number

Z = None

Mass, charge, neutron number

decay_channels = None

decay channels if any

has_redist = None

(bool) particle has an energy redistribution

is_alias = None

(bool) particle is an alias (PDG ID encodes special scoring behavior)

is_baryon = None

(bool) particle is a baryon

is_charged = None

(bool) particle is a lepton

is_em = None

(bool) if it’s an electromagnetic particle

is_hadron = None

(bool) particle is a hadron (meson or baryon)

is_lepton = None

(bool) particle is a lepton

is_meson = None

(bool) particle is a meson

is_nucleus = None

(bool) particle is a nucleus

is_stable = None

(bool) particle is stable

lifetime = None

(float) lifetime

mass = None

Mass in atomic units or GeV

ncoid = None

Neucosma ID of particle

princeidx = None

(int) Prince index (in state vector)

sl
Return the slice for this species on the grid
can be used as spec[s.sl]
Returns:a slice object pointing to the species in the state vecgtor
Return type:(slice)
sname = None

(str) species name in string representation

class prince_cr.data.SpeciesManager(ncoid_list, ed)[source]

Provides a database with particle and species.

add_grid(grid_tag, dimension)[source]

Defines additional grid dimensions under a certain tag.

Propagates changes to this variable to all known species.

ncoid2princeidx = None

(dict) Converts Neucosma ID to index in state vector

nspec = None

(int) Total number of species

princeidx2ncoid = None

(dict) Converts index in state vector to Neucosma ID

princeidx2sref = None

(dict) Converts prince index to reference of class:data.PrinceSpecies

sname2princeidx = None

(dict) Converts particle name to index in state vector

sname2sref = None

(dict) Converts particle name to reference of class:data.PrinceSpecies

prince_cr.data.db_handler = <prince_cr.data.PrinceDB object>

db_handler is the HDF file interface

prince_cr.solvers – PDE solver implementations

Contains solvers to solve the coupled differential equation system

The steps performed by the solver are:

\Phi_{i + 1} = \Delta X_i\boldsymbol{M}_{int} \cdot \Phi_i + \frac{\Delta X_i}{\rho(X_i)}\cdot\boldsymbol{M}_{dec} \cdot \Phi_i)

Contains solvers, i.e. integrators, kernels, steppers, for PriNCe.

class prince_cr.solvers.propagation.UHECRPropagationResult(state, egrid, spec_man)[source]

Reduced version of solver class, that only holds the result vector and defined add and multiply

get_lnA(nco_ids, egrid=None)[source]

Return the average ln(A) as a function of total energy for all elements in the range

get_solution(nco_id)[source]

Returns the spectrum in energy per nucleon

get_solution_group(nco_ids, epow=3, egrid=None)[source]

Return the summed spectrum (in total energy) for all elements in the range

get_solution_scale(nco_id, epow=0)[source]

Returns the spectrum scaled back to total energy

class prince_cr.solvers.partial_diff.SemiLagrangianSolver(cr_grid)[source]

Contains routines to project spectra from shifted grids back to old grid

interpolate(conloss, state)[source]

Uses linear interpolation to find the new state old grid

interpolate_4thorder_weights(conloss, state)[source]

Uses quadratic interpolation with lagrange polynomials

interpolate_5thorder_weights(conloss, state)[source]

Uses cubic interpolation with lagrange polynomials

interpolate_cubic_weights(conloss, state)[source]

Uses cubic interpolation with lagrange polynomials

interpolate_gradient(conloss, state)[source]

Uses a linear approximation arround x_i to find the new state old grid

interpolate_linear_weights(conloss, state)[source]

Uses linear interpolation with lagrange polynomials (same as interpolate, but directly implemented for testing)

interpolate_quadratic_weights(conloss, state)[source]

Uses quadratic interpolation with lagrange polynomials

prince_cr.cross_sections – Cross section data management

Contains function to load and combined cross section models

prince_cr.interaction_rates – Computation of Interaction Matrices

Contains function to precompute the sparse Interaction matrices efficiently

The module contains classes for computations of interaction rates

class prince_cr.interaction_rates.ContinuousAdiabaticLossRate(prince_run, energy='grid', *args, **kwargs)[source]

Implementation of continuous pair production loss rates.

loss_vector(z, energy=None)[source]

Returns all continuous losses on dim_states grid

single_loss_length(pid, z)[source]

Returns energy loss length in cm (convenience function for plotting)

spec_man = None

Reference to species manager

class prince_cr.interaction_rates.ContinuousPairProductionLossRate(prince_run, energy='grid', *args, **kwargs)[source]

Implementation of continuous pair production loss rates.

loss_vector(z)[source]

Returns all continuous losses on dim_states grid

photon_vector(z)[source]

Returns photon vector at redshift z on photon grid.

This vector is in fact a matrix of vectors of the interpolated photon field with dimensions (dim_cr, xi_steps).

Parameters:z (float) – redshift

Return value from cache if redshift value didn’t change since last call.

single_loss_length(pid, z, pfield=None)[source]

Returns energy loss length in cm (convenience function for plotting)

photon_field = None

Reference to PhotonField object

spec_man = None

Reference to species manager

class prince_cr.interaction_rates.PhotoNuclearInteractionRate(prince_run=None, with_dense_jac=True, *args, **kwargs)[source]

Implementation of photo-hadronic/nuclear interaction rates. This Version directly writes the data into a CSC-matrix and only updates the data each time.

get_hadr_jacobian(z, scale_fac=1.0, force_update=False)[source]

Returns the nonel rate vector and coupling matrix.

photon_vector(z)[source]

Returns photon vector at redshift z on photon grid.

This vector is in fact a matrix of vectors of the interpolated photon field with dimensions (dim_cr, xi_steps).

Parameters:z (float) – redshift

Return value from cache if redshift value didn’t change since last call.

single_interaction_length(pid, z, pfield=None)[source]

Returns energy loss length in cm (convenience function for plotting)

cross_sections = None

Reference to CrossSection object

photon_field = None

Reference to PhotonField object

spec_man = None

Reference to species manager

prince_cr.photonfields – EBL and CMB photon fields

Contains different EBL models as a function of redshift

Created on Feb 22, 2017

@author: Anatoli Fedynitch

class prince_cr.photonfields.CIBDominguez2D(model='base', simple_scaling=False)[source]

CIB model “3” by Gilmore et al.

CIB photon distribution for z = 0…2. Requires availability of an scipy.interp2d object file data/CIB_dominguez_int2D.ppo.

Note: The class contains an interpolators for the upper and lower limits,
which are not yet accessable through a function
Ref.:
R.C. Gilmore et al., MNRAS 410, 2556 (2011) [arXiv:1104.0671]
class prince_cr.photonfields.CIBFranceschini2D(simple_scaling=False)[source]

CIB model “1” by Fraceschini et al.

CIB photon distribution for z = 0…2. Requires availability of an scipy.interp2d object file data/CIB_franceschini_int2D.ppo.

Ref.:
  1. Franceschini et al., Astron. Astrphys. 487, 837 (2008) [arXiv:0805.1841]
class prince_cr.photonfields.CIBFranceschiniZ0[source]

CIB model “1” by Fraceschini et al.

CIB photon distribution at z=0.

Ref.:
  1. Franceschini et al., Astron. Astrphys. 487, 837 (2008) [arXiv:0805.1841]
get_photon_density(E, z)[source]

Returns the redshift-scaled number density of CMB photons

Parameters:
  • z (float) – redshift
  • E (float) – photon energy (GeV)
Returns:

CMB photon spectrum in

System Message: WARNING/2 ({\rm GeV}}^{-1} {\rm cm}}^{-3})

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Return type:

float
class prince_cr.photonfields.CIBGilmore2D(model='fiducial', simple_scaling=False)[source]

CIB model “3” by Gilmore et al.

CIB photon distribution for z = 0…7. Requires availability of an scipy.interp2d object file data/CIB_gilmore_int2D.ppo.

Note: Currently uses the fixed model from the reference as standard,
for the fiducial model, change the ‘model’ keyword
Ref.:
R.C. Gilmore et al., MNRAS Soc. 422, 3189 (2012) [arXiv:1104.0671]
class prince_cr.photonfields.CIBInoue2D(model='base', simple_scaling=False)[source]

CIB model “2” by Inoue et al.

CIB photon distribution for z = 0…10. Requires availability of an scipy.interp2d object file data/CIB_inoue_int2D.ppo. A low and high variation of the “third-population” component are also available, by passing

Ref.:
  1. Inoue et al. [arXiv:1212.1683]
class prince_cr.photonfields.CIBSteckerZ0[source]

CIB model “1” by Stecker et al.

CIB photon distribution at z=0.

Ref.:
F.W. Stecker et al., Astrophys. J. 648, 774 (2006) [astro-ph/0510449]
get_photon_density(E, z)[source]

Returns the redshift-scaled number density of CMB photons

Parameters:
  • z (float) – redshift
  • E (float) – photon energy (GeV)
Returns:

CMB photon spectrum in

System Message: WARNING/2 ({\rm GeV}}^{-1} {\rm cm}}^{-3})

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Return type:

float
class prince_cr.photonfields.CMBPhotonSpectrum[source]

Redshift-scaled number density of CMB photons

In the CMB frame (equivalent to the observer’s frame). Normalisation from Planck’s spectrum. The scaling goes as n(E,z) = (1+z)^3 n(E/(1+z), z = 0). The CMB spectrum is a blackbody spectrum with the present-day temperature T0 = 2.725 K.

Ref.:
  1. Ahlers, L.A. Anchordoqui, and S. Sarkar, Phys. Rev. D 79, 083009 (2009) [0902.3993]
get_photon_density(E, z)[source]

Returns the redshift-scaled number density of CMB photons

Parameters:
  • z (float) – redshift
  • E (float) – photon energy (GeV)
Returns:

CMB photon spectrum in

System Message: WARNING/2 ({\rm GeV}}^{-1} {\rm cm}}^{-3})

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Return type:

float
class prince_cr.photonfields.CombinedPhotonField(list_of_classes_and_args)[source]

Class to combine (sum) several models, which inherit from PhotonField.

This class is useful when constructing a realistic photon spectrum, which is typically a superposition of CMB and CIB. The list of models can be passed to the constructor or each model can be added separately using the add_model().

Parameters:list_of_classes_and_args – Can be either list of classes or list of tuples (class, args)
add_model(model_class, model_args=())[source]

Adds a model class to the combination.

get_photon_density(E, z)[source]

Returns the redshift-scaled number density of photons as a sum of different models.

Parameters:
  • z (float) – redshift
  • E (float) – photon energy (GeV)
Returns:

CMB photon spectrum in

System Message: WARNING/2 ({\rm GeV}}^{-1} {\rm cm}}^{-3})

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Return type:

float
class prince_cr.photonfields.EBLSplined2D[source]
get_photon_density(E, z)[source]

Returns the redshift-scaled number density of CIB photons

Accepts scalar, vector and matrix arguments.

Parameters:
  • z (float) – redshift
  • E (float) – photon energy (GeV)
Returns:

CMB photon spectrum in

System Message: WARNING/2 ({\rm GeV}}^{-1} {\rm cm}}^{-3})

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Return type:

float
class prince_cr.photonfields.FlatPhotonSpectrum[source]

Constant photon density for testing.

get_photon_density(E, z)[source]

Returns the redshift-scaled number density of CMB photons

Parameters:
  • z (float) – redshift
  • E (float) – photon energy (GeV)
Returns:

CMB photon spectrum in

System Message: WARNING/2 ({\rm GeV}}^{-1} {\rm cm}}^{-3})

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Return type:

float
class prince_cr.photonfields.PhotonField[source]

Base class for constructing target photon densities.

Derived classes have to implement the method PhotonField.get_photon_densities().

prince_cr.cr_sources – UHECR source class definitions

Defines the (simple) source injection for the extragalactic propagation

Defines source models for cosmic ray propagation

The standard interface requires to UHECRSolvers requires that each source defines a methods injection_rate(self, z)

class prince_cr.cr_sources.AugerFitSource(prince_run, ncoids=None, params=None, norm=1.0, m='flat', *args, **kwargs)[source]

Simple source class with spectral index and rigidity dependent cutoff Defined to be parrallel for all species below the cutoff as in Auger Combined Fit paper

if E < Z * Rcut:
inj(E) = norm * E**-gamma
else:
inj(E) = norm * E**-gamma * exp(- E / Z * Rcut)

params defined as {pid: gamma, Rcut, norm}

injection_spectrum(pid, energy, params)[source]

Prototype to be defined in each child class

class prince_cr.cr_sources.RigdityCutoffSource(prince_run, ncoids=None, params=None, norm=1.0, m='flat', *args, **kwargs)[source]

Simple source class with spectral index and rigidity dependent cutoff

inj(E) = norm * E**-gamma * exp(- E / Z * Rcut)

params defined as {pid: gamma, Rcut, norm}

injection_spectrum(pid, energy, params)[source]

Prototype to be defined in each child class

class prince_cr.cr_sources.RigidityFlexSource(prince_run, ncoids=None, params=None, norm=1.0, m='flat', *args, **kwargs)[source]

Simple source class with spectral index and rigidity dependent cutoff Parameter alpha to scaled the rigidity dependence

inj(E) = norm * E**-gamma * exp(- E / Z**alpha * Rcut)

params defined as {pid: gamma, Rcut, alpha, norm}

injection_spectrum(pid, energy, params)[source]

Prototype to be defined in each child class

class prince_cr.cr_sources.SimpleSource(prince_run, ncoids=None, params=None, norm=1.0, m='flat', *args, **kwargs)[source]

Simple source class with spectral index and cutoff

inj(E) = norm * E**-gamma * exp(- E / Emax)

params defined as {pid: gamma, Emax, norm}

injection_spectrum(pid, energy, params)[source]

Prototype to be defined in each child class

class prince_cr.cr_sources.SpectrumSource(prince_run, ncoids=None, params=None, norm=1.0, m='flat', *args, **kwargs)[source]

Source class with the spectrum defined externally by an array The spectrum might be interpolated as needed

params defined as {pid: egrid, specgrid}

injection_spectrum(pid, energy, params)[source]

Prototype to be defined in each child class