Grid

class zdm.grid.Grid(survey, state, zDMgrid, zvals, dmvals, smear_mask, wdist=None, prev_grid=None)[source]

Bases: object

2D grid for computing FRB detection rates as a function of z and DM.

The Grid class is the core computational object in zdm. It builds a 2D probability distribution representing expected FRB detection rates across the redshift-DM plane for a given survey and parameter set.

Assumptions: - Each z bin represents FRBs originating at that redshift (not integrated) - Linear uniform spacing in both z and DM - DM includes cosmic + host contributions convolved together

rates

2D array of expected FRB rates per (z, DM) bin.

Type:

ndarray

zvals

Redshift bin centers.

Type:

ndarray

dmvals

DM bin centers in pc/cm^3.

Type:

ndarray

state

Parameter state used for grid calculation.

Type:

parameters.State

survey

Associated survey object.

Type:

survey.Survey

Methods Summary

EF([alpha, bandwidth])

Calculates the fluence--energy conversion factors as a function of redshift This does NOT account for the central frequency

GenMCFRB(Emax_boost)

Generates a single FRB according to the grid distributions

GenMCSample(N[, Poisson])

Generate a MC sample of FRB events

build_sz()

calc_dV([reINIT])

Calculates volume per steradian probed by a survey.

calc_pdv([beam_b, beam_o])

Calculates the rate per cell. Assumed model: a power-law between Emin and Emax (erg) with slope gamma. Efficiencies: list of efficiency response to DM So-far: does NOT include time x solid-angle factor.

calc_rates()

multiplies the rate per cell with the appropriate pdm plot

calc_thresholds(F0, eff_table[, bandwidth, ...])

Sets the effective survey threshold on the zdm grid

check_grid([TOLERANCE])

Check that the grid values are behaving as expected

chk_upd_param(param, vparams[, update])

Check to see whether a parameter is differs from that in self.state

get_dm_coeffs(DMlist)

Returns indices and coefficients for interpolating between DM values

get_p_zgdm(DMs)

Calcuates the probability of redshift given a DM We already have our grid of observed DM values.

get_pw_dist()

Function asking the grid to return the p(w) distribution.

get_rates()

Returns rates, multiplied by the relevant constant, and accounting for any DM preference via a DM mask

get_z_coeffs(zlist)

Returns indices and coefficients for interpolating between z values

initMC()

Initialises the MC sample, if it has not been doen already This uses a great deal of RAM - hence, do not do this lightly!

init_luminosity_functions()

Set the luminsoity function for FRB energetics

load_grid(gridfile, zfile, dmfile)

parse_grid(zDMgrid, zvals, dmvals)

set_evolution()

Scales volumetric rate by SFR

smear_dm(smear)

Smears DM using the supplied array.

update(vparams[, ALL, prev_grid])

Update the grid based on a set of input parameters

Methods Documentation

EF(alpha=0, bandwidth=1000000000.0)[source]

Calculates the fluence–energy conversion factors as a function of redshift This does NOT account for the central frequency

GenMCFRB(Emax_boost)[source]

Generates a single FRB according to the grid distributions

Samples beam position b, FRB DM, z, s=SNR/SNRth, and w Currently: no interpolation included. This should be implemented in s,DM, and z.

NOTE: currently, the actual FRB widths are not part of ‘grid’

only the relative probabilities of any given width. Hence, this routine only returns the integer of the width bin not the width itelf.

Parameters:

  • pwb (optional) – probability(width,beam)

  • Emax_boost (float, optional) – Allow for larger energies than Emax The factor is logarithmic, i.e. Emax_boost = 2. allows for 10**2 higher energies than Emax

Returns:

FRBparams=[MCz,MCDM,MCb,j,MCs], pwb values These are:

MCz: redshift MCDM: dispersion measure (extragalactic) MCb: beam value j: MCs: SNR/SNRth value of FRB MCw: width value of FRB

[MCz, MCDM, MCb, j, MCs, MCw]

Return type:

tuple

GenMCSample(N, Poisson=False)[source]

Generate a MC sample of FRB events

If Poisson=True, then interpret N as a Poisson expectation value Otherwise, generate precisely N FRBs

Generated values are [MCz, MCDM, MCb, MCs, MCw] NOTE: the routine GenMCFRB does not know ‘w’, merely

which w bin it generates.

build_sz()[source]
calc_dV(reINIT=False)[source]

Calculates volume per steradian probed by a survey.

Does this only in the z-dimension (for obvious reasons!)

calc_pdv(beam_b=None, beam_o=None)[source]

Calculates the rate per cell. Assumed model: a power-law between Emin and Emax (erg)

with slope gamma.

Efficiencies: list of efficiency response to DM So-far: does NOT include time x solid-angle factor

NOW: this includes a solid-angle and beam factor if initialised

This will recalculate beam factors if they are passed, however during iteration this is not recalculated

calc_rates()[source]

multiplies the rate per cell with the appropriate pdm plot

calc_thresholds(F0: float, eff_table, bandwidth=1000000000.0, nuRef=1300000000.0, weights=None)[source]

Sets the effective survey threshold on the zdm grid

Parameters:

  • F0 (float) – base survey threshold

  • eff_table ([type]) – table of efficiencies corresponding to DM-values. 1, 2, or 3 dimensions!

  • bandwidth ([type], optional) – [description]. Defaults to 1e9.

  • nuObs ([float], optional) – survey frequency (affects sensitivity via alpha - only for alpha method) Defaults to 1.3e9.

  • nuRef ([float], optional) – reference frequency we are calculating thresholds at Defaults to 1.3e9.

  • weights ([type], optional) – [description]. Defaults to None.

Raises:
check_grid(TOLERANCE=1e-06)[source]

Check that the grid values are behaving as expected

TOLERANCE: defines the max relative difference in expected

and found values that will be tolerated

chk_upd_param(param: str, vparams: dict, update=False)[source]

Check to see whether a parameter is differs from that in self.state

Parameters:

  • param (str) – Paramter in question

  • vparams (dict) – Dict holding the value

  • update (bool, optional) – If True, update the value in self.state. Defaults to False.

Returns:

True if the parameter is different

Return type:

bool

get_dm_coeffs(DMlist)[source]

Returns indices and coefficients for interpolating between DM values

dmlist: np.ndarray of dispersion measures (extragalactic!)

get_p_zgdm(DMs: ndarray)[source]

Calcuates the probability of redshift given a DM We already have our grid of observed DM values. Just take slices!

Parameters:

DMs (np.ndarray) – array of DM values

Returns:

array of priors for the DMs

Return type:

np.ndarray

get_pw_dist()[source]

Function asking the grid to return the p(w) distribution.

This will be an “all-burst” distribution in case of a repeater inherited class.

Note that a grid does not actually know what a “width” means: it is simply an abstract category of FRBs corresponding to a particular efficiency and fraction of the population.

Args: None

Returns:

Rate per width bin Wzs (np.ndarray: Nw x Nz): Rate as a function of w and z Wdms (np.ndarray: Nw x Ndm): Rate as a function of w and DM

Return type:

Wtots (np.ndarray)

get_rates()[source]

Returns rates, multiplied by the relevant constant, and accounting for any DM preference via a DM mask

get_z_coeffs(zlist)[source]

Returns indices and coefficients for interpolating between z values

zlist: np.ndarray of dispersion measures (extragalactic!)

initMC()[source]

Initialises the MC sample, if it has not been doen already This uses a great deal of RAM - hence, do not do this lightly!

init_luminosity_functions()[source]

Set the luminsoity function for FRB energetics

load_grid(gridfile, zfile, dmfile)[source]
parse_grid(zDMgrid, zvals, dmvals)[source]
set_evolution()[source]

Scales volumetric rate by SFR

smear_dm(smear: ndarray)[source]

Smears DM using the supplied array. Example use: DMX contribution

smear_grid is created in place

Parameters:

smear (np.ndarray) – Smearing array

update(vparams: dict, ALL=False, prev_grid=None)[source]

Update the grid based on a set of input parameters

Hierarchy: Each indent corresponds to one ‘level’. This is used in the program control below to dictate how far each tree should proceed in calculation. Direct variable inputs are always listed first We see that sfr evolution and dm smearing lie just before the pdv step Hence, we deal with these first, and calc rates as a final step regardless of what else has changed.

Parameters:

  • vparams (dict) – dict containing the parameters to be updated and their values

  • prev_grid (Grid, optional) – If provided, it is assumed this grid has been updated on items that need not be repeated for the current grid. i.e. Speed up!

  • ALL (bool, optional) – If True, update the full grid

calc_rates:
calc_pdv

Emin Emax gamma H0 calc_thresholds

F0 alpha bandwidth

set_evolution

sfr_n H0

smear_grid

grid mask

dmx_params (lmean, lsigma)

dV zdm_grid

H0

Note that the grid is independent of the constant C (trivial dependence)

Parameters:

vparams (dict) – [description]

__init__(survey, state, zDMgrid, zvals, dmvals, smear_mask, wdist=None, prev_grid=None)[source]

Initialize the Grid for a survey and parameter state.

Parameters:

  • survey (survey.Survey) – Survey object with telescope properties and FRB data.

  • state (parameters.State) – Parameter state defining the model. Note: grids share the same State object, so modifications affect all grids.

  • zDMgrid (ndarray) – 2D array of p(DM|z) probabilities, shape (nz, ndm).

  • zvals (ndarray) – Redshift bin centers. Bins span [z - dz/2, z + dz/2].

  • dmvals (ndarray) – DM bin centers in pc/cm^3. Bins span [DM - dDM/2, DM + dDM/2].

  • smear_mask (ndarray) – 1D convolution kernel for host DM smearing.

  • wdist (bool, optional) – If True, include width distribution effects.

  • prev_grid (Grid, optional) – Another Grid with same z/DM values but different survey. Allows reusing pre-computed cosmological quantities.

init_luminosity_functions()[source]

Set the luminsoity function for FRB energetics

parse_grid(zDMgrid, zvals, dmvals)[source]
load_grid(gridfile, zfile, dmfile)[source]
get_dm_coeffs(DMlist)[source]

Returns indices and coefficients for interpolating between DM values

dmlist: np.ndarray of dispersion measures (extragalactic!)

get_z_coeffs(zlist)[source]

Returns indices and coefficients for interpolating between z values

zlist: np.ndarray of dispersion measures (extragalactic!)

check_grid(TOLERANCE=1e-06)[source]

Check that the grid values are behaving as expected

TOLERANCE: defines the max relative difference in expected

and found values that will be tolerated

calc_dV(reINIT=False)[source]

Calculates volume per steradian probed by a survey.

Does this only in the z-dimension (for obvious reasons!)

EF(alpha=0, bandwidth=1000000000.0)[source]

Calculates the fluence–energy conversion factors as a function of redshift This does NOT account for the central frequency

set_evolution()[source]

Scales volumetric rate by SFR

calc_pdv(beam_b=None, beam_o=None)[source]

Calculates the rate per cell. Assumed model: a power-law between Emin and Emax (erg)

with slope gamma.

Efficiencies: list of efficiency response to DM So-far: does NOT include time x solid-angle factor

NOW: this includes a solid-angle and beam factor if initialised

This will recalculate beam factors if they are passed, however during iteration this is not recalculated

get_pw_dist()[source]

Function asking the grid to return the p(w) distribution.

This will be an “all-burst” distribution in case of a repeater inherited class.

Note that a grid does not actually know what a “width” means: it is simply an abstract category of FRBs corresponding to a particular efficiency and fraction of the population.

Args: None

Returns:

Rate per width bin Wzs (np.ndarray: Nw x Nz): Rate as a function of w and z Wdms (np.ndarray: Nw x Ndm): Rate as a function of w and DM

Return type:

Wtots (np.ndarray)

calc_rates()[source]

multiplies the rate per cell with the appropriate pdm plot

get_rates()[source]

Returns rates, multiplied by the relevant constant, and accounting for any DM preference via a DM mask

calc_thresholds(F0: float, eff_table, bandwidth=1000000000.0, nuRef=1300000000.0, weights=None)[source]

Sets the effective survey threshold on the zdm grid

Parameters:

  • F0 (float) – base survey threshold

  • eff_table ([type]) – table of efficiencies corresponding to DM-values. 1, 2, or 3 dimensions!

  • bandwidth ([type], optional) – [description]. Defaults to 1e9.

  • nuObs ([float], optional) – survey frequency (affects sensitivity via alpha - only for alpha method) Defaults to 1.3e9.

  • nuRef ([float], optional) – reference frequency we are calculating thresholds at Defaults to 1.3e9.

  • weights ([type], optional) – [description]. Defaults to None.

Raises:
smear_dm(smear: ndarray)[source]

Smears DM using the supplied array. Example use: DMX contribution

smear_grid is created in place

Parameters:

smear (np.ndarray) – Smearing array

get_p_zgdm(DMs: ndarray)[source]

Calcuates the probability of redshift given a DM We already have our grid of observed DM values. Just take slices!

Parameters:

DMs (np.ndarray) – array of DM values

Returns:

array of priors for the DMs

Return type:

np.ndarray

GenMCSample(N, Poisson=False)[source]

Generate a MC sample of FRB events

If Poisson=True, then interpret N as a Poisson expectation value Otherwise, generate precisely N FRBs

Generated values are [MCz, MCDM, MCb, MCs, MCw] NOTE: the routine GenMCFRB does not know ‘w’, merely

which w bin it generates.

initMC()[source]

Initialises the MC sample, if it has not been doen already This uses a great deal of RAM - hence, do not do this lightly!

GenMCFRB(Emax_boost)[source]

Generates a single FRB according to the grid distributions

Samples beam position b, FRB DM, z, s=SNR/SNRth, and w Currently: no interpolation included. This should be implemented in s,DM, and z.

NOTE: currently, the actual FRB widths are not part of ‘grid’

only the relative probabilities of any given width. Hence, this routine only returns the integer of the width bin not the width itelf.

Parameters:

  • pwb (optional) – probability(width,beam)

  • Emax_boost (float, optional) – Allow for larger energies than Emax The factor is logarithmic, i.e. Emax_boost = 2. allows for 10**2 higher energies than Emax

Returns:

FRBparams=[MCz,MCDM,MCb,j,MCs], pwb values These are:

MCz: redshift MCDM: dispersion measure (extragalactic) MCb: beam value j: MCs: SNR/SNRth value of FRB MCw: width value of FRB

[MCz, MCDM, MCb, j, MCs, MCw]

Return type:

tuple

build_sz()[source]
update(vparams: dict, ALL=False, prev_grid=None)[source]

Update the grid based on a set of input parameters

Hierarchy: Each indent corresponds to one ‘level’. This is used in the program control below to dictate how far each tree should proceed in calculation. Direct variable inputs are always listed first We see that sfr evolution and dm smearing lie just before the pdv step Hence, we deal with these first, and calc rates as a final step regardless of what else has changed.

Parameters:

  • vparams (dict) – dict containing the parameters to be updated and their values

  • prev_grid (Grid, optional) – If provided, it is assumed this grid has been updated on items that need not be repeated for the current grid. i.e. Speed up!

  • ALL (bool, optional) – If True, update the full grid

calc_rates:
calc_pdv

Emin Emax gamma H0 calc_thresholds

F0 alpha bandwidth

set_evolution

sfr_n H0

smear_grid

grid mask

dmx_params (lmean, lsigma)

dV zdm_grid

H0

Note that the grid is independent of the constant C (trivial dependence)

Parameters:

vparams (dict) – [description]

chk_upd_param(param: str, vparams: dict, update=False)[source]

Check to see whether a parameter is differs from that in self.state

Parameters:

  • param (str) – Paramter in question

  • vparams (dict) – Dict holding the value

  • update (bool, optional) – If True, update the value in self.state. Defaults to False.

Returns:

True if the parameter is different

Return type:

bool