API ¶

class cosmoprimo.cosmology.BaseBackground(engine)¶

Base background engine, including a few definitions.

Omega_Lambda(z)¶: Density of cosmological constant, unitless.

Omega_b(z)¶: Density parameter of baryons, unitless.

Omega_cdm(z)¶: Density parameter of cold dark matter, unitless.

Omega_de(z)¶: Density of total dark energy (fluid + cosmological constant), unitless.

Omega_fld(z)¶: Density of cosmological constant, unitless.

Omega_g(z)¶: Density parameter of photons, unitless.

Omega_k(z)¶: Density parameter of curvature, unitless.

Omega_m(z)¶: Density parameter of non-relativistic (matter-like) component, including non-relativistic part of massive neutrino, unitless.

Omega_ncdm(z)¶: Density parameter of massive neutrinos, unitless. If species is None returned shape is (N_ncdm,) if z is a scalar, else (N_ncdm, len(z)). Else if species is between 0 and N_ncdm, return density for this species.

Omega_ncdm_tot(z)¶: Total density parameter of massive neutrinos, unitless.

Omega_pncdm(z, species=None)¶: Density parameter of pressure of non-relativistic part of massive neutrinos, unitless. If species is None returned shape is (N_ncdm,) if z is a scalar, else (N_ncdm, len(z)). Else if species is between 0 and N_ncdm, return density for this species.

Omega_pncdm_tot(z)¶: Total density parameter of pressure of non-relativistic part of massive neutrinos, unitless.

Omega_r(z)¶: Density parameter of relativistic (radiation-like) component, including relativistic part of massive neutrino and massless neutrino, unitless.

Omega_ur(z)¶: Density parameter of ultra relativistic neutrinos, unitless.

T_cmb(z)¶: The CMB temperature, in \(K\).

T_ncdm(z)¶: Return the ncdm temperature (massive neutrinos), in \(K\). Returned shape is (N_ncdm,) if z is a scalar, else (N_ncdm, len(z)).

efunc(z)¶: Function giving \(E(z)\), where the Hubble parameter is defined as \(H(z) = H_{0} E(z)\), unitless.

hubble_function(z)¶: Hubble function ba.index_bg_H, in \(\mathrm{km}/\mathrm{s}/\mathrm{Mpc}\).

p_ncdm(z, species=None)¶: Pressure of non-relativistic part of massive neutrinos for each species, in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\). If species is None returned shape is (N_ncdm,) if z is a scalar, else (N_ncdm, len(z)). Else if species is between 0 and N_ncdm, return pressure for this species.

p_ncdm_tot(z)¶: Total pressure of non-relativistic part of massive neutrinos, in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_Lambda(z)¶: Comoving density of cosmological constant \(\rho_{\Lambda}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_b(z)¶: Comoving density of baryons \(\rho_{b}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_cdm(z)¶: Comoving density of cold dark matter \(\rho_{cdm}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_crit(z)¶

Comoving critical density excluding curvature \(\rho_{c}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

This is defined as:

\[\rho_{\mathrm{crit}}(z) = \frac{3 H(z)^{2}}{8 \pi G}.\]

rho_de(z)¶: Total comoving density of dark energy \(\rho_{\mathrm{de}}\) (fluid + cosmological constant), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_fld(z)¶: Comoving density of dark energy fluid \(\rho_{\mathrm{fld}}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_g(z)¶: Comoving density of photons \(\rho_{g}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_k(z)¶: Comoving density of curvature \(\rho_{k}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_m(z)¶: Comoving density of matter \(\rho_{m}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_ncdm(z, species=None)¶: Comoving density of non-relativistic part of massive neutrinos for each species, in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\). If species is None returned shape is (N_ncdm,) if z is a scalar, else (N_ncdm, len(z)). Else if species is between 0 and N_ncdm, return density for this species.

rho_ncdm_tot(z)¶: Total comoving density of non-relativistic part of massive neutrinos, in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_r(z)¶: Comoving density of radiation \(\rho_{r}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_tot(z)¶: Comoving total density \(\rho_{\mathrm{tot}}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_ur(z)¶: Comoving density of ultra-relativistic radiation (massless neutrinos) \(\rho_{ur}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

class cosmoprimo.cosmology.BaseEngine(extra_params=None, **params)¶

Bases: cosmoprimo.utils.BaseClass

Base engine for cosmological calculation.

Initialize engine.

Parameters

extra_params (dict, default=None) – Extra engine parameters, typically precision parameters.
params (dict) – Engine parameters.

get(*args, **kwargs)¶: Return an input (or easily derived) parameter.

get_background()¶: Return Background calculations.

get_fourier()¶: Return Fourier calculations.

get_harmonic()¶: Return Harmonic calculations.

get_perturbations()¶: Return Perturbations calculations.

get_primordial()¶: Return Primordial calculations.

get_thermodynamics()¶: Return Thermodynamics calculations.

get_transfer()¶: Return Transfer calculations.

class cosmoprimo.cosmology.BaseSection(engine)¶

Bases: object

Base section.

class cosmoprimo.cosmology.Cosmology(engine=None, extra_params=None, **params)¶

Cosmology, defined as a set of parameters (and possibly a current engine attached to it).

Initialize Cosmology.

Note

Massive neutrinos can be provided e.g. through m_ncdm or Omega_ncdm/omega_ncdm with their temperatures w.r.t. CMB T_ncdm_over_cmb. In the case of Omega_ncdm, the neutrino energy density (see _compute_ncdm_momenta()) will be inverted to recover m_ncdm. If a single value for m_ncdm or Omega_ncdm is provided, neutrino_hierarchy can be set to None (default, single massive neutrino) or ‘normal’, ‘inverted’, ‘degenerate’ (all neutrinos with same mass), which will determine the masses of the 3 neutrinos. If the number of relativistic species N_ur is not provided (or None), it will be determined from the desired effective number of neutrinos N_eff (typically kept at 3.044 for 3 neutrinos whatever m_ncdm or Omega_ncdm/omega_ncdm) and the number of massless neutrinos (\(m \leq 0.00017\)), which are then removed from the list m_ncdm. Parameter Omega_ncdm/omega_ncdm (accessed as cosmo['Omega_ncdm']/cosmo['omega_ncdm']) will always provide the total energy density of neutrinos (single value). The pivot scale k_pivot is in \(\mathrm{Mpc}^{-1}\).`

Parameters

engine (string, default=None) – Engine name, one of [‘class’, ‘camb’, ‘eisenstein_hu’, ‘eisenstein_hu_nowiggle’, ‘bbks’]. If None, no engine is set.
extra_params (dict, default=None) – Extra engine parameters, typically precision parameters.
params (dict) – Cosmological and calculation parameters which take priority over the default ones.

clone(engine=None, extra_params=None, **params)¶

Clone current cosmology instance, optionally updating engine and parameters.

Parameters

engine (string, default=None) – Engine name, one of [‘class’, ‘camb’, ‘eisenstein_hu’, ‘eisenstein_hu_nowiggle’, ‘bbks’]. If None, use same engine (class) as current instance.
extra_params (dict, default=None) – Extra engine parameters, typically precision parameters.
params (dict) – Cosmological and calculation parameters which take priority over the current ones.

Returns

new – Copy of current instance, with updated engine and parameters.

Return type

Cosmology

classmethod from_state(state)¶: Instantiate and initalise class with state dictionary.

get(*args, **kwargs)¶: Return an input (or easily derived) parameter.

get_background(engine=None, set_engine=True, **extra_params)¶

Get background.

Parameters

engine (string, default=None) – Engine name, one of [‘class’, ‘camb’, ‘eisenstein_hu’, ‘eisenstein_hu_nowiggle’, ‘bbks’]. If None, returns current Cosmology.engine.
set_engine (bool, default=True) – Whether to attach returned engine to cosmology. (Set False if e.g. you want to use this engine for a single calculation).
extra_params (dict) – Extra engine parameters, typically precision parameters.

classmethod get_default_parameters(of=None, include_conflicts=True)¶

Return default input parameters.

Parameters

of (string, default=None) – One of [‘cosmology’,’calculation’]. If None, returns all parameters.
include_conflicts (bool, default=True) – Whether to include conflicting parameters (then all accepted parameters).

Returns

params – Dictionary of default parameters.

Return type

dict

get_fourier(engine=None, set_engine=True, **extra_params)¶

Get fourier.

Parameters

engine (string, default=None) – Engine name, one of [‘class’, ‘camb’, ‘eisenstein_hu’, ‘eisenstein_hu_nowiggle’, ‘bbks’]. If None, returns current Cosmology.engine.
set_engine (bool, default=True) – Whether to attach returned engine to cosmology. (Set False if e.g. you want to use this engine for a single calculation).
extra_params (dict) – Extra engine parameters, typically precision parameters.

get_harmonic(engine=None, set_engine=True, **extra_params)¶

Get harmonic.

Parameters

engine (string, default=None) – Engine name, one of [‘class’, ‘camb’, ‘eisenstein_hu’, ‘eisenstein_hu_nowiggle’, ‘bbks’]. If None, returns current Cosmology.engine.
set_engine (bool, default=True) – Whether to attach returned engine to cosmology. (Set False if e.g. you want to use this engine for a single calculation).
extra_params (dict) – Extra engine parameters, typically precision parameters.

get_perturbations(engine=None, set_engine=True, **extra_params)¶

Get perturbations.

Parameters

engine (string, default=None) – Engine name, one of [‘class’, ‘camb’, ‘eisenstein_hu’, ‘eisenstein_hu_nowiggle’, ‘bbks’]. If None, returns current Cosmology.engine.
set_engine (bool, default=True) – Whether to attach returned engine to cosmology. (Set False if e.g. you want to use this engine for a single calculation).
extra_params (dict) – Extra engine parameters, typically precision parameters.

get_primordial(engine=None, set_engine=True, **extra_params)¶

Get primordial.

Parameters

engine (string, default=None) – Engine name, one of [‘class’, ‘camb’, ‘eisenstein_hu’, ‘eisenstein_hu_nowiggle’, ‘bbks’]. If None, returns current Cosmology.engine.
set_engine (bool, default=True) – Whether to attach returned engine to cosmology. (Set False if e.g. you want to use this engine for a single calculation).
extra_params (dict) – Extra engine parameters, typically precision parameters.

get_thermodynamics(engine=None, set_engine=True, **extra_params)¶

Get thermodynamics.

Parameters

engine (string, default=None) – Engine name, one of [‘class’, ‘camb’, ‘eisenstein_hu’, ‘eisenstein_hu_nowiggle’, ‘bbks’]. If None, returns current Cosmology.engine.
set_engine (bool, default=True) – Whether to attach returned engine to cosmology. (Set False if e.g. you want to use this engine for a single calculation).
extra_params (dict) – Extra engine parameters, typically precision parameters.

get_transfer(engine=None, set_engine=True, **extra_params)¶

Get transfer.

Parameters

engine (string, default=None) – Engine name, one of [‘class’, ‘camb’, ‘eisenstein_hu’, ‘eisenstein_hu_nowiggle’, ‘bbks’]. If None, returns current Cosmology.engine.
set_engine (bool, default=True) – Whether to attach returned engine to cosmology. (Set False if e.g. you want to use this engine for a single calculation).
extra_params (dict) – Extra engine parameters, typically precision parameters.

classmethod load(filename)¶: Load class from disk.

save(filename)¶: Save class to disk.

set_engine(engine, set_engine=True, **extra_params)¶

Set engine for cosmological calculation.

Parameters

engine (string) – Engine name, one of [‘class’, ‘camb’, ‘eisenstein_hu’, ‘eisenstein_hu_nowiggle’, ‘bbks’].
set_engine (bool, default=True) – Whether to attach returned engine to cosmology. (Set False if e.g. you want to use this engine for a single calculation).
extra_params (dict) – Extra engine parameters, typically precision parameters.

exception cosmoprimo.cosmology.CosmologyError¶

Bases: Exception

Exception raised by Cosmology.

with_traceback()¶: Exception.with_traceback(tb) – set self.__traceback__ to tb and return self.

cosmoprimo.cosmology.Fourier(cosmology, engine=None, set_engine=True, **extra_params)¶

Return Fourier calculations.

Parameters

cosmology (Cosmology) – Current cosmology.
engine (string, default=None) – Engine name, one of [‘class’, ‘camb’, ‘eisenstein_hu’, ‘eisenstein_hu_nowiggle’, ‘bbks’]. If None, returns current Cosmology.engine.
set_engine (bool, default=True) – Whether to attach returned engine to cosmology (Set False if e.g. you want to use this engine for a single calculation).
extra_params (dict) – Extra engine parameters, typically precision parameters.

Returns

engine

Return type

cosmoprimo.cosmology.Harmonic(cosmology, engine=None, set_engine=True, **extra_params)¶

Return Harmonic calculations.

Parameters

cosmology (Cosmology) – Current cosmology.
engine (string, default=None) – Engine name, one of [‘class’, ‘camb’, ‘eisenstein_hu’, ‘eisenstein_hu_nowiggle’, ‘bbks’]. If None, returns current Cosmology.engine.
set_engine (bool, default=True) – Whether to attach returned engine to cosmology (Set False if e.g. you want to use this engine for a single calculation).
extra_params (dict) – Extra engine parameters, typically precision parameters.

Returns

engine

Return type

cosmoprimo.cosmology.Perturbations(cosmology, engine=None, set_engine=True, **extra_params)¶

Return Perturbations calculations.

Parameters

cosmology (Cosmology) – Current cosmology.
engine (string, default=None) – Engine name, one of [‘class’, ‘camb’, ‘eisenstein_hu’, ‘eisenstein_hu_nowiggle’, ‘bbks’]. If None, returns current Cosmology.engine.
set_engine (bool, default=True) – Whether to attach returned engine to cosmology (Set False if e.g. you want to use this engine for a single calculation).
extra_params (dict) – Extra engine parameters, typically precision parameters.

Returns

engine

Return type

cosmoprimo.cosmology.Primordial(cosmology, engine=None, set_engine=True, **extra_params)¶

Return Primordial calculations.

Parameters

cosmology (Cosmology) – Current cosmology.
engine (string, default=None) – Engine name, one of [‘class’, ‘camb’, ‘eisenstein_hu’, ‘eisenstein_hu_nowiggle’, ‘bbks’]. If None, returns current Cosmology.engine.
set_engine (bool, default=True) – Whether to attach returned engine to cosmology (Set False if e.g. you want to use this engine for a single calculation).
extra_params (dict) – Extra engine parameters, typically precision parameters.

Returns

engine

Return type

class cosmoprimo.cosmology.RegisteredEngine(name, bases, class_dict)¶

Bases: type

Metaclass registering BaseEngine-derived classes.

mro()¶: Return a type’s method resolution order.

cosmoprimo.cosmology.Thermodynamics(cosmology, engine=None, set_engine=True, **extra_params)¶

Return Thermodynamics calculations.

Parameters

cosmology (Cosmology) – Current cosmology.
engine (string, default=None) – Engine name, one of [‘class’, ‘camb’, ‘eisenstein_hu’, ‘eisenstein_hu_nowiggle’, ‘bbks’]. If None, returns current Cosmology.engine.
set_engine (bool, default=True) – Whether to attach returned engine to cosmology (Set False if e.g. you want to use this engine for a single calculation).
extra_params (dict) – Extra engine parameters, typically precision parameters.

Returns

engine

Return type

cosmoprimo.cosmology.Transfer(cosmology, engine=None, set_engine=True, **extra_params)¶

Return Transfer calculations.

Parameters

cosmology (Cosmology) – Current cosmology.
engine (string, default=None) – Engine name, one of [‘class’, ‘camb’, ‘eisenstein_hu’, ‘eisenstein_hu_nowiggle’, ‘bbks’]. If None, returns current Cosmology.engine.
set_engine (bool, default=True) – Whether to attach returned engine to cosmology (Set False if e.g. you want to use this engine for a single calculation).
extra_params (dict) – Extra engine parameters, typically precision parameters.

Returns

engine

Return type

https://github.com/bccp/nbodykit/blob/master/nbodykit/cosmology/cosmology.py

cosmoprimo.cosmology.check_params(args)¶: Check for conflicting parameters in args parameter dictionary.

cosmoprimo.cosmology.compile_params(args)¶

Compile parameters args: - normalise parameter names - perform immediate parameter derivations (e.g. omega => Omega) - set neutrino masses if relevant

Parameters: args (dict) – Input parameter dictionary, without parameter conflicts.
Returns: params – Normalised parameter dictionary.
Return type: dict

References

cosmoprimo.cosmology.find_conflicts(name)¶

Return conflicts corresponding to input parameter name.

Parameters: name (string) – Parameter name.
Returns: conflicts – Conflicting parameter names.
Return type: tuple

cosmoprimo.cosmology.get_engine(engine)¶

Return engine (class) for cosmological calculation.

Parameters: engine (BaseEngine, string) – Engine or one of [‘class’, ‘camb’, ‘eisenstein_hu’, ‘eisenstein_hu_nowiggle’, ‘bbks’].
Returns: engine
Return type: BaseEngine

cosmoprimo.cosmology.merge_params(args, moreargs)¶

Merge moreargs parameters into args. moreargs parameters take priority over those defined in args.

Note

args is modified in-place.

Parameters

args (dict) – Base parameter dictionary.
moreargs (dict) – Parameter dictionary to be merged into args.

Returns

args – Merged parameter dictionary.

Return type

dict

Engines¶

CLASS¶

Cosmological calculation with the Boltzmann code CLASS.

class cosmoprimo.classy.ClassEngine(*args: Any, **kwargs: Any)¶

Bases: pyclass.ClassEngine, cosmoprimo.cosmology.BaseEngine

Engine for the Boltzmann code CLASS.

Initialize engine.

Parameters

extra_params (dict, default=None) – Extra engine parameters, typically precision parameters.
params (dict) – Engine parameters.

get(*args, **kwargs)¶: Return an input (or easily derived) parameter.

get_background()¶: Return Background calculations.

get_fourier()¶: Return Fourier calculations.

get_harmonic()¶: Return Harmonic calculations.

get_perturbations()¶: Return Perturbations calculations.

get_primordial()¶: Return Primordial calculations.

get_thermodynamics()¶: Return Thermodynamics calculations.

get_transfer()¶: Return Transfer calculations.

class cosmoprimo.classy.Fourier(*args: Any, **kwargs: Any)¶

Bases: pyclass.Fourier

pk_interpolator(nonlinear=False, of='delta_m', **kwargs)¶

Return PowerSpectrumInterpolator2D instance.

Parameters

nonlinear (bool, default=False) – Whether to return the nonlinear power spectrum (if requested in parameters, with ‘nonlinear’:’halofit’ or ‘HMcode’). Computed only for of == 'delta_m' or ‘delta_cb’.
of (string, tuple, default='delta_m') – Perturbed quantities. Either ‘delta_m’ for matter perturbations or ‘delta_cb’ for cold dark matter + baryons perturbations will use precomputed spectra. Else, e.g. (‘delta_m’,’theta_cb’) for the cross matter density - cold dark matter + baryons velocity power spectra, are computed on-the-fly.
kwargs (dict) – Arguments for PowerSpectrumInterpolator2D.

pk_kz(k, z, nonlinear=False, of='m')¶

Return power spectrum, in \((\mathrm{Mpc}/h)^{3}\), using original CLASS routine.

Parameters

k (array_like) – Wavenumbers, in \(h/\mathrm{Mpc}\).
z (array_like) – Redshifts.
nonlinear (bool, default=False) – Whether to return the nonlinear power spectrum (if requested in parameters, with ‘nonlinear’:’halofit’ or ‘HMcode’).
of (string, default='delta_m') – Perturbed quantities. Either ‘delta_m’ for matter perturbations or ‘delta_cb’ for cold dark matter + baryons perturbations.

Returns

pk – Power spectrum array of shape (len(k),len(z)).

Return type

array

property sigma8_cb¶: Current r.m.s. of cold dark matter + baryons perturbations in a sphere of \(8 \mathrm{Mpc}/h\) unitless.

property sigma8_m¶: Current r.m.s. of matter perturbations in a sphere of \(8 \mathrm{Mpc}/h\), unitless.

sigma8_z(z, of='delta_m')¶: Return the r.m.s. of of perturbations in sphere of \(8 \mathrm{Mpc}/h\).

sigma_rz(r, z, of='delta_m', **kwargs)¶: Return the r.m.s. of of perturbations in sphere of \(r \mathrm{Mpc}/h\).

table(nonlinear=False, of='delta_m')¶

Return power spectrum table, in \((\mathrm{Mpc}/h)^{3}\).

Parameters

nonlinear (bool, default=False) – Whether to return the nonlinear power spectrum (if requested in parameters, with ‘nonlinear’:’halofit’ or ‘HMcode’). Computed only for of == 'delta_m' or ‘delta_cb’.
of (string, tuple, default='delta_m') – Perturbed quantities. Either ‘delta_m’ for matter perturbations or ‘delta_cb’ for cold dark matter + baryons perturbations will use precomputed spectra. Else, e.g. (‘delta_m’,’theta_cb’) for the cross matter density - cold dark matter + baryons velocity power spectra, are computed on-the-fly.

Returns

k (array) – Wavenumbers.
z (array) – Redshifts.
pk (array) – Power spectrum array of shape (len(k),len(z)).

class cosmoprimo.classy.Harmonic(*args: Any, **kwargs: Any)¶

Bases: pyclass.Harmonic

lensed_table(ellmax=- 1, of=None)¶

Return table of lensed \(C_{\ell}\), unitless.

Parameters

ellmax (int, default=-1) – Maximum \(\ell\) desired. If negative, is relative to the requested maximum \(\ell\).
of (list, default=None) – List of outputs, [‘tt’,’ee’,’bb’,’pp’,’te’,’tp’]. If None, return all computed outputs.

Returns

cell – Structured array.

Return type

array

unlensed_table(ellmax=- 1, of=None)¶

Return table of unlensed \(C_{\ell}\) (i.e. CMB power spectra without lensing and lensing potentials), unitless.

Parameters

ellmax (int, default=-1) – Maximum \(\ell\) desired. If negative, is relative to the requested maximum \(\ell\).
of (list, default=None) – List of outputs, [‘tt’,’ee’,’bb’,’te’,’pp’,’tp’,’ep’]. If None, return all computed outputs.

Returns

cell – Structured array.

Return type

array

Note

Normalisation is \(C_{\ell}\) rather than \(\ell(\ell+1)C_{\ell}/(2\pi)\) (or \(\ell^{2}(\ell+1)^{2}/(2\pi)\) in the case of the lensing potential pp spectrum). Usually multiplied by CMB temperature in \(\mu K\).

class cosmoprimo.classy.Primordial(*args: Any, **kwargs: Any)¶

Bases: pyclass.Primordial

property A_s¶: Scalar amplitude of the primordial power spectrum at \(k_\mathrm{pivot}\), unitless.

property ln_1e10_A_s¶: \(\ln(10^{10}A_s)\), unitless.

pk_interpolator(mode='scalar')¶

Return power spectrum interpolator.

Parameters: mode (string, default='scalar') – ‘scalar’, ‘vector’ or ‘tensor’ mode.
Returns: interp – PowerSpectrumInterpolator1D instance if only one type of initial conditions (typically adiabatic), else dictionary of class:PowerSpectrumInterpolator1D corresponding to the tuples of initial conditions.
Return type: PowerSpectrumInterpolator1D, dict

pk_k(k, mode='scalar')¶

The primordial spectrum of curvature perturbations at k, generated by inflation, in \((\mathrm{Mpc}/h)^{3}\). For scalar perturbations this is e.g. defined as:

\[\mathcal{P_R}(k) = A_s \left (\frac{k}{k_0} \right )^{n_s - 1 + 1/2 \ln(k/k_0) (dn_s / d\ln k)}\]

CAMB¶

Cosmological calculation with the Boltzmann code CAMB.

class cosmoprimo.camb.Background(engine)¶

Bases: cosmoprimo.cosmology.BaseBackground

Omega_Lambda(z)¶: Density of cosmological constant, unitless.

Omega_b(z)¶: Density parameter of baryons, unitless.

Omega_cdm(z)¶: Density parameter of cold dark matter, unitless.

Omega_de(z)¶: Total density of dark energy (fluid + cosmological constant), unitless.

Omega_fld(z)¶: Density of cosmological constant, unitless.

Omega_g(z)¶: Density parameter of photons, unitless.

Omega_k(z)¶: Density parameter of curvature, unitless.

Omega_m(z)¶: Density parameter of non-relativistic (matter-like) component, including non-relativistic part of massive neutrino, unitless.

Omega_ncdm(z)¶: Density parameter of massive neutrinos, unitless. If species is None returned shape is (N_ncdm,) if z is a scalar, else (N_ncdm, len(z)). Else if species is between 0 and N_ncdm, return density for this species.

Omega_ncdm_tot(z)¶: Total density parameter of massive neutrinos, unitless.

Omega_pncdm(z, species=None)¶: Density parameter of pressure of non-relativistic part of massive neutrinos, unitless. If species is None returned shape is (N_ncdm,) if z is a scalar, else (N_ncdm, len(z)). Else if species is between 0 and N_ncdm, return density for this species.

Omega_pncdm_tot(z)¶: Total density parameter of pressure of non-relativistic part of massive neutrinos, unitless.

Omega_r(z)¶: Density parameter of relativistic (radiation-like) component, including relativistic part of massive neutrino and massless neutrino, unitless.

Omega_ur(z)¶: Density parameter of ultra relativistic neutrinos, unitless.

T_cmb(z)¶: The CMB temperature, in \(K\).

T_ncdm(z)¶: Return the ncdm temperature (massive neutrinos), in \(K\). Returned shape is (N_ncdm,) if z is a scalar, else (N_ncdm, len(z)).

angular_diameter_distance(z)¶

Proper angular diameter distance, in \(\mathrm{Mpc}/h\).

See eq. 18 of astro-ph/9905116 for \(D_{A}(z)\).

comoving_angular_distance(z)¶

Comoving angular distance, in \(\mathrm{Mpc}/h\).

See eq. 16 of astro-ph/9905116 for \(D_{M}(z)\).

comoving_radial_distance(z)¶

Comoving radial distance, in \(mathrm{Mpc}/h\).

See eq. 15 of astro-ph/9905116 for \(D_C(z)\).

efunc(z)¶: Function giving \(E(z)\), where the Hubble parameter is defined as \(H(z) = H_{0} E(z)\), unitless.

hubble_function(z)¶: Hubble function, in \(\mathrm{km}/\mathrm{s}/\mathrm{Mpc}\).

luminosity_distance(z)¶

Luminosity distance, in \(\mathrm{Mpc}/h\).

See eq. 21 of astro-ph/9905116 for \(D_{L}(z)\).

p_ncdm(z, species=None)¶: Pressure of non-relativistic part of massive neutrinos for each species, in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\). If species is None returned shape is (N_ncdm,) if z is a scalar, else (N_ncdm, len(z)). Else if species is between 0 and N_ncdm, return pressure for this species.

p_ncdm_tot(z)¶: Total pressure of non-relativistic part of massive neutrinos, in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_Lambda(z)¶: Comoving density of cosmological constant \(\rho_{\Lambda}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_b(z)¶: Density parameter of baryons, unitless.

rho_cdm(z)¶: Comoving density of cold dark matter \(\rho_{cdm}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_crit(z)¶

Comoving critical density excluding curvature \(\rho_{c}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

This is defined as:

\[\rho_{\mathrm{crit}}(z) = \frac{3 H(z)^{2}}{8 \pi G}.\]

rho_de(z)¶: Comoving total density of dark energy \(\rho_{\mathrm{de}}\) (fluid + cosmological constant), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_fld(z)¶: Comoving density of dark energy fluid \(\rho_{\mathrm{fld}}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_g(z)¶: Comoving density of photons \(\rho_{g}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_k(z)¶: Comoving density of curvature \(\rho_{k}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_m(z)¶: Comoving density of matter \(\rho_{m}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_ncdm(z, species=None)¶: Comoving density of non-relativistic part of massive neutrinos for each species, in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\). If species is None returned shape is (N_ncdm,) if z is a scalar, else (N_ncdm, len(z)). Else if species is between 0 and N_ncdm, return density for this species.

rho_ncdm_tot(z)¶: Total comoving density of non-relativistic part of massive neutrinos \(\rho_{ncdm}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_r(z)¶: Comoving density of radiation \(\rho_{r}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_tot(z)¶: Comoving total density \(\rho_{\mathrm{tot}}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_ur(z)¶: Comoving density of ultra-relativistic radiation (massless neutrinos) \(\rho_{ur}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

time(z)¶: Proper time (age of universe), in \(\mathrm{Gy}\).

class cosmoprimo.camb.CambEngine(*args, **kwargs)¶

Engine for the Boltzmann code CAMB.

Initialize engine.

Parameters

extra_params (dict, default=None) – Extra engine parameters, typically precision parameters.
params (dict) – Engine parameters.

compute(tasks)¶

The main function, which executes the desired modules.

Parameters: tasks (list, string) – Calculation to perform, in the following list: [‘background’, ‘thermodynamics’, ‘transfer’, ‘harmonic’, ‘lensing’, ‘fourier’]

get(*args, **kwargs)¶: Return an input (or easily derived) parameter.

get_background()¶: Return Background calculations.

get_fourier()¶: Return Fourier calculations.

get_harmonic()¶: Return Harmonic calculations.

get_perturbations()¶: Return Perturbations calculations.

get_primordial()¶: Return Primordial calculations.

get_thermodynamics()¶: Return Thermodynamics calculations.

get_transfer()¶: Return Transfer calculations.

class cosmoprimo.camb.Fourier(engine)¶

pk_interpolator(nonlinear=False, of='delta_m', **kwargs)¶

Return PowerSpectrumInterpolator2D instance.

Parameters

nonlinear (bool, default=False) – Whether to return the nonlinear power spectrum (if requested in parameters, with ‘nonlinear’:’halofit’ or ‘HMcode’). Computed only for of == ‘delta_m’.
of (string, tuple, default='delta_m') – Perturbed quantities. Does not make difference between ‘theta_cb’ and ‘theta_m’.
kwargs (dict) – Arguments for PowerSpectrumInterpolator2D.

pk_kz(k, z, nonlinear=False, of='delta_m')¶

Return power spectrum, in \((\mathrm{Mpc}/h)^{3}\).

Parameters

k (array_like) – Wavenumbers, in \(h/\mathrm{Mpc}\).
z (array_like) – Redshifts.
nonlinear (bool, default=False) – Whether to return the nonlinear power spectrum (if requested in parameters, with ‘nonlinear’:’halofit’ or ‘HMcode’).
of (string, default='delta_m') – Perturbed quantities. Does not make difference between ‘theta_cb’ and ‘theta_m’.

Returns

pk – Power spectrum array of shape (len(k),len(z)).

Return type

array

property sigma8_m¶: Current r.m.s. of matter perturbations in a sphere of \(8 \mathrm{Mpc}/h\), unitless.

sigma8_z(z, of='delta_m')¶: Return the r.m.s. of of perturbations in sphere of \(8 \mathrm{Mpc}/h\).

sigma_rz(r, z, of='delta_m', **kwargs)¶: Return the r.m.s. of of perturbations in sphere of \(r \mathrm{Mpc}/h\).

table(nonlinear=False, of='m')¶

Return power spectrum table, in \((\mathrm{Mpc}/h)^{3}\).

Parameters

nonlinear (bool, default=False) – Whether to return the nonlinear power spectrum (if requested in parameters, with ‘nonlinear’:’halofit’ or ‘HMcode’). Computed only for of == ‘delta_m’ or ‘delta_cb’.
of (string, tuple, default='delta_m') – Perturbed quantities. Does not make difference between ‘theta_cb’ and ‘theta_m’.

Returns

k (array) – Wavenumbers.
z (array) – Redshifts.
pk (array) – Power spectrum array of shape (len(k),len(z)).

class cosmoprimo.camb.Harmonic(engine)¶

lens_potential_cl(ellmax=- 1)¶: Return potential \(C_{\ell}\) [‘pp’,’tp’,’ep’], unitless.

lensed_cl(ellmax=- 1)¶: Return lensed \(C_{\ell}\) [‘tt’,’ee’,’bb’,’te’], unitless.

unlensed_cl(ellmax=- 1)¶: Return unlensed \(C_{\ell}\) [‘tt’,’ee’,’bb’,’te’], unitless.

class cosmoprimo.camb.Primordial(engine)¶

https://arxiv.org/abs/astro-ph/0507263

property A_s¶: Scalar amplitude of the primordial power spectrum at \(k_\mathrm{pivot}\), unitless.

property k_pivot¶: Primordial power spectrum pivot scale, where the primordial power is equal to \(A_{s}\), in \(h/\mathrm{Mpc}\).

property ln_1e10_A_s¶: \(\ln(10^{10}A_s)\), unitless.

property n_s¶: Power-law index i.e. tilt of the primordial power spectrum, unitless.

pk_interpolator(mode='scalar')¶

Return power spectrum interpolator.

Parameters: mode (string, default='scalar') – ‘scalar’, ‘vector’ or ‘tensor’ mode.
Returns: interp
Return type: PowerSpectrumInterpolator1D

pk_k(k, mode='scalar')¶

The primordial spectrum of curvature perturbations at k, generated by inflation, in \((\mathrm{Mpc}/h)^{3}\). For scalar perturbations this is e.g. defined as:

\[\mathcal{P_R}(k) = A_s \left (\frac{k}{k_0} \right )^{n_s - 1 + 1/2 \ln(k/k_0) (dn_s / d\ln k)}\]

Eisenstein & Hu¶

class cosmoprimo.eisenstein_hu.Background(engine)¶

Bases: cosmoprimo.cosmology.BaseBackground

Background quantities.

Note

Does not treat neutrinos.

Omega_Lambda(z)¶: Density of cosmological constant, unitless.

Omega_b(z)¶: Density parameter of baryons, unitless.

Omega_cdm(z)¶: Density parameter of cold dark matter, unitless.

Omega_de(z)¶: Density of total dark energy (fluid + cosmological constant), unitless.

Omega_fld(z)¶: Density of cosmological constant, unitless.

Omega_g(z)¶: Density parameter of photons, unitless.

Omega_k(z)¶: Density parameter of curvature, unitless.

Omega_m(z)¶: Density parameter of non-relativistic (matter-like) component, including non-relativistic part of massive neutrino, unitless.

Omega_ncdm(z)¶: Density parameter of massive neutrinos, unitless. If species is None returned shape is (N_ncdm,) if z is a scalar, else (N_ncdm, len(z)). Else if species is between 0 and N_ncdm, return density for this species.

Omega_ncdm_tot(z)¶: Total density parameter of massive neutrinos, unitless.

Omega_pncdm(z, species=None)¶: Density parameter of pressure of non-relativistic part of massive neutrinos, unitless. If species is None returned shape is (N_ncdm,) if z is a scalar, else (N_ncdm, len(z)). Else if species is between 0 and N_ncdm, return density for this species.

Omega_pncdm_tot(z)¶: Total density parameter of pressure of non-relativistic part of massive neutrinos, unitless.

Omega_r(z)¶: Density parameter of relativistic (radiation-like) component, including relativistic part of massive neutrino and massless neutrino, unitless.

Omega_ur(z)¶: Density parameter of ultra relativistic neutrinos, unitless.

T_cmb(z)¶: The CMB temperature, in \(K\).

T_ncdm(z)¶: Return the ncdm temperature (massive neutrinos), in \(K\). Returned shape is (N_ncdm,) if z is a scalar, else (N_ncdm, len(z)).

efunc(z)¶: Function giving \(E(z)\), where the Hubble parameter is defined as \(H(z) = H_{0} E(z)\), unitless.

growth_factor(z)¶

Approximation of growth factor.

References

https://arxiv.org/abs/astro-ph/9709112, eq. 4 https://ui.adsabs.harvard.edu/abs/1992ARA%26A..30..499C/abstract, eq. 29

growth_rate(z)¶

Approximation of growth rate.

References

hubble_function(z)¶: Hubble function ba.index_bg_H, in \(\mathrm{km}/\mathrm{s}/\mathrm{Mpc}\).

p_ncdm(z, species=None)¶: Pressure of non-relativistic part of massive neutrinos for each species, in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\). If species is None returned shape is (N_ncdm,) if z is a scalar, else (N_ncdm, len(z)). Else if species is between 0 and N_ncdm, return pressure for this species.

p_ncdm_tot(z)¶: Total pressure of non-relativistic part of massive neutrinos, in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_Lambda(z)¶: Comoving density of cosmological constant \(\rho_{\Lambda}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_b(z)¶: Comoving density of baryons \(\rho_{b}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_cdm(z)¶: Comoving density of cold dark matter \(\rho_{cdm}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_crit(z)¶

Comoving critical density excluding curvature \(\rho_{c}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

This is defined as:

\[\rho_{\mathrm{crit}}(z) = \frac{3 H(z)^{2}}{8 \pi G}.\]

rho_de(z)¶: Total comoving density of dark energy \(\rho_{\mathrm{de}}\) (fluid + cosmological constant), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_fld(z)¶: Comoving density of dark energy fluid \(\rho_{\mathrm{fld}}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_g(z)¶: Comoving density of photons \(\rho_{g}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_k(z)¶: Comoving density of curvature \(\rho_{k}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_m(z)¶: Comoving density of matter \(\rho_{m}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_ncdm(z, species=None)¶: Comoving density of non-relativistic part of massive neutrinos for each species, in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\). If species is None returned shape is (N_ncdm,) if z is a scalar, else (N_ncdm, len(z)). Else if species is between 0 and N_ncdm, return density for this species.

rho_ncdm_tot(z)¶: Total comoving density of non-relativistic part of massive neutrinos, in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_r(z)¶: Comoving density of radiation \(\rho_{r}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_tot(z)¶: Comoving total density \(\rho_{\mathrm{tot}}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

rho_ur(z)¶: Comoving density of ultra-relativistic radiation (massless neutrinos) \(\rho_{ur}\), in \(10^{10} M_{\odot}/h / (\mathrm{Mpc}/h)^{3}\).

class cosmoprimo.eisenstein_hu.EisensteinHuEngine(*args, **kwargs)¶

https://arxiv.org/abs/astro-ph/9709112

Implementation of Eisenstein & Hu analytic formulae.

References

Initialize engine.

Parameters

extra_params (dict, default=None) – Extra engine parameters, typically precision parameters.
params (dict) – Engine parameters.

compute()¶: Precompute coefficients for the transfer function.

get(*args, **kwargs)¶: Return an input (or easily derived) parameter.

get_background()¶: Return Background calculations.

get_fourier()¶: Return Fourier calculations.

get_harmonic()¶: Return Harmonic calculations.

get_perturbations()¶: Return Perturbations calculations.

get_primordial()¶: Return Primordial calculations.

get_thermodynamics()¶: Return Thermodynamics calculations.

get_transfer()¶: Return Transfer calculations.

class cosmoprimo.eisenstein_hu.Fourier(engine)¶

pk_interpolator(of='delta_m', ignore_norm=False, **kwargs)¶

Return PowerSpectrumInterpolator2D instance.

Parameters

of (string, tuple) – Perturbed quantities: ‘delta_m’, ‘theta_m’. No distinction is made between baryons and CDM. Requesting velocity divergence ‘theta_xx’ will rescale the power spectrum by the growth rate as a function of z.
ignore_norm (bool) – Whether to ignore power spectrum normalisation. If False, sigma8 should be provided as part of the parameters.
kwargs (dict) – Arguments for PowerSpectrumInterpolator2D.

property sigma8_m¶: Current r.m.s. of matter perturbations in a sphere of \(8 \mathrm{Mpc}/h\), unitless.

sigma8_z(z, of='delta_m')¶: Return the r.m.s. of of perturbations in sphere of \(8 \mathrm{Mpc}/h\). No distinction is made between baryons and CDM.

sigma_rz(r, z, of='delta_m', **kwargs)¶: Return the r.m.s. of of perturbations in sphere of \(r \mathrm{Mpc}/h\). No distinction is made between baryons and CDM.

class cosmoprimo.eisenstein_hu.Primordial(engine)¶

Initialize Primordial.

class cosmoprimo.eisenstein_hu.Thermodynamics(engine)¶

Initialize Thermodynamics.

class cosmoprimo.eisenstein_hu.Transfer(engine)¶

https://arxiv.org/abs/astro-ph/9709112

transfer_k(k, frac_baryon=None)¶

Return matter transfer function.

Parameters

k (array_like) – Wavenumbers.
frac_baryon (float, default=None) – If not None, scale the baryon transfer function w.r.t. to the CDM one. May be useful to remove BAO.

Returns

transfer

Return type

array

Eisenstein & Hu no-wiggle¶

class cosmoprimo.eisenstein_hu_nowiggle.EisensteinHuNoWiggleEngine(*args, **kwargs)¶

Bases: cosmoprimo.eisenstein_hu.EisensteinHuEngine

Implementation of Eisenstein & Hu no-wiggle analytic formulae.

References

Initialize engine.

Parameters

extra_params (dict, default=None) – Extra engine parameters, typically precision parameters.
params (dict) – Engine parameters.

compute()¶: Precompute coefficients for the transfer function.

get(*args, **kwargs)¶: Return an input (or easily derived) parameter.

get_background()¶: Return Background calculations.

get_fourier()¶: Return Fourier calculations.

get_harmonic()¶: Return Harmonic calculations.

get_perturbations()¶: Return Perturbations calculations.

get_primordial()¶: Return Primordial calculations.

get_thermodynamics()¶: Return Thermodynamics calculations.

get_transfer()¶: Return Transfer calculations.

class cosmoprimo.eisenstein_hu_nowiggle.Transfer(engine)¶

transfer_k(k)¶

Return matter transfer function.

Parameters: k (array_like) – Wavenumbers.
Returns: transfer
Return type: array

BBKS¶

class cosmoprimo.bbks.BBKSEngine(*args, **kwargs)¶

https://ui.adsabs.harvard.edu/abs/1986ApJ…304…15B/abstract https://arxiv.org/abs/astro-ph/9412025 https://arxiv.org/abs/1812.05995

Implementation of BBKS no-wiggle analytic formulae.

References

Initialize engine.

Parameters

extra_params (dict, default=None) – Extra engine parameters, typically precision parameters.
params (dict) – Engine parameters.

compute()¶: Precompute coefficients for the transfer function.

get(*args, **kwargs)¶: Return an input (or easily derived) parameter.

get_background()¶: Return Background calculations.

get_fourier()¶: Return Fourier calculations.

get_harmonic()¶: Return Harmonic calculations.

get_perturbations()¶: Return Perturbations calculations.

get_primordial()¶: Return Primordial calculations.

get_thermodynamics()¶: Return Thermodynamics calculations.

get_transfer()¶: Return Transfer calculations.

class cosmoprimo.bbks.Transfer(engine)¶

https://github.com/Samreay/Barry/blob/master/barry/cosmology/power_spectrum_smoothing.py

transfer_k(k)¶

Return matter transfer function.

Parameters: k (array_like) – Wavenumbers.
Returns: transfer
Return type: array

Utilities¶

BAO filter¶

Different techniques to extra BAO from the power spectrum of correlation function. For the power spectrum, the most accurate one is Wallish2018PowerSpectrumBAOFilter. For the correlation function: Kirkby2013CorrelationFunctionBAOFilter.

class cosmoprimo.bao_filter.BaseCorrelationFunctionBAOFilter(xi_interpolator, cosmo=None, **kwargs)¶

Bases: cosmoprimo.utils.BaseClass

Base BAO filter for correlation function.

Run BAO filter.

Parameters

xi_interpolator (CorrelationFunctionInterpolator1D, CorrelationFunctionInterpolator2D) – Input correlation function to remove BAO peak from.
cosmo (Cosmology, default=None) – Cosmology instance, which may be used to tune filter settings (depending on rs_drag).
kwargs (dict) – Arguments for set_s().

property cosmo¶: Cosmology.

rs_drag_ratio()¶: If cosmo is provided, return the ratio of its rs_drag to the fiducial one (from Cosmology()), else 1.

set_s(ns=1024)¶

Set separations where to evaluate the correlation function (between xi_interpolator.extrap_smin and xi_interpolator.extrap_smax).

Parameters: ns (int, default=1024) – Number of separations.

smooth_pk_interpolator(**kwargs)¶

Return smooth (i.e. no-wiggle) power spectrum using FFTlog.

Parameters: kwargs (dict) – Override interpolation and extrapolation settings of return power spectrum interpolator.
Returns: interp – 1D or 2D depending on pk_interpolator.
Return type: PowerSpectrumInterpolator1D, PowerSpectrumInterpolator2D

smooth_xi_interpolator(**kwargs)¶

Return smooth (i.e. no-peak) correlation function.

Parameters: kwargs (dict) – Override interpolation settings of xi_interpolator.
Returns: interp – 1D or 2D depending on xi_interpolator.
Return type: CorrelationFunctionInterpolator1D, CorrelationFunctionInterpolator2D

class cosmoprimo.bao_filter.BasePowerSpectrumBAOFilter(pk_interpolator, cosmo=None, **kwargs)¶

Bases: cosmoprimo.utils.BaseClass

Base BAO filter for power spectrum.

Run BAO filter.

Parameters

pk_interpolator (PowerSpectrumInterpolator1D, PowerSpectrumInterpolator2D) – Input power spectrum to remove BAO wiggles from.
cosmo (Cosmology, default=None) – Cosmology instance, which may be used to tune filter settings (depending on rs_drag).
kwargs (dict) – Arguments for set_k().

property cosmo¶: Cosmology.

rs_drag_ratio()¶: If cosmo is provided, return the ratio of its rs_drag to the fiducial one (from Cosmology()), else 1.

set_k(nk=1024)¶

Set wavenumbers where to evaluate the power spectrum (between pk_interpolator.extrap_kmin and pk_interpolator.extrap_kmax).

Parameters: nk (int, default=1024) – Number of wavenumbers.

smooth_pk_interpolator(**kwargs)¶

Return smooth (i.e. no-wiggle) power spectrum.

Parameters: kwargs (dict) – Override interpolation and extrapolation settings of pk_interpolator.
Returns: interp – 1D or 2D depending on pk_interpolator.
Return type: PowerSpectrumInterpolator1D, PowerSpectrumInterpolator2D

smooth_xi_interpolator(**kwargs)¶

Return smooth (i.e. no-peak) correlation function using FFTlog.

Parameters: kwargs (dict) – Override interpolation and extrapolation settings of returned correlation function interpolator.
Returns: interp – 1D or 2D depending on pk_interpolator.
Return type: CorrelationFunctionInterpolator1D, CorrelationFunctionInterpolator2D

property wiggles¶: Extracted wiggles.

cosmoprimo.bao_filter.CorrelationFunctionBAOFilter(xi_interpolator, engine='kirkby2013', **kwargs)¶: Run correlation function BAO filter corresponding to the provided engine.

class cosmoprimo.bao_filter.EHNoWigglePolyPowerSpectrumBAOFilter(pk_interpolator, kbox=(0.005, 0.5), dampkbox=(0.01, 0.4), dampsigma=10, rescale_kbox=True, cosmo=None, **kwargs)¶

Bases: cosmoprimo.bao_filter.BasePowerSpectrumBAOFilter

Remove BAO wiggles using the Eisenstein & Hu no-wiggle analytic formula, emulated with a 6-th order polynomial.

Run BAO filter.

Parameters

pk_interpolator (PowerSpectrumInterpolator1D, PowerSpectrumInterpolator2D) – Input power spectrum to remove BAO wiggles from.
kbox (tuple, default=(5e-3, 0.5)) – k-range to fit the Eisenstein & Hu no-wiggle power spectrum to the input one pk_interpolator.
dampkbox (tuple, default=(1e-2, 0.4)) – k-range to interpolate between the Eisenstein & Hu no-wiggle power spectrum and the input one pk_interpolator with an Gaussian damping factor.
dampsigma (float, default=10) – Standard deviation of the Gaussian damping factor.
rescale_kbox (bool, default=True) – Whether to rescale kbox and dampkbox by the ratio of rs_drag relative to the fiducial cosmology (may help robustify the procedure for cosmologies far from the fiducial one).
cosmo (Cosmology, default=None) – Cosmology instance, used to compute the Eisenstein & Hu no-wiggle power spectrum.
kwargs (dict) – Arguments for set_k().

compute()¶: Run filter.

property cosmo¶: Cosmology.

rs_drag_ratio()¶: If cosmo is provided, return the ratio of its rs_drag to the fiducial one (from Cosmology()), else 1.

set_k(nk=1024)¶

Set wavenumbers where to evaluate the power spectrum (between pk_interpolator.extrap_kmin and pk_interpolator.extrap_kmax).

Parameters: nk (int, default=1024) – Number of wavenumbers.

smooth_pk_interpolator(**kwargs)¶

Return smooth (i.e. no-wiggle) power spectrum.

Parameters: kwargs (dict) – Override interpolation and extrapolation settings of pk_interpolator.
Returns: interp – 1D or 2D depending on pk_interpolator.
Return type: PowerSpectrumInterpolator1D, PowerSpectrumInterpolator2D

smooth_xi_interpolator(**kwargs)¶

Return smooth (i.e. no-peak) correlation function using FFTlog.

Parameters: kwargs (dict) – Override interpolation and extrapolation settings of returned correlation function interpolator.
Returns: interp – 1D or 2D depending on pk_interpolator.
Return type: CorrelationFunctionInterpolator1D, CorrelationFunctionInterpolator2D

property wiggles¶: Extracted wiggles.

class cosmoprimo.bao_filter.Hinton2017PowerSpectrumBAOFilter(pk_interpolator, degree=13, sigma=1, weight=0.5, **kwargs)¶

Bases: cosmoprimo.bao_filter.BasePowerSpectrumBAOFilter

Power spectrum BAO filter consisting in fitting a high degree polynomial to the input power spectrum in log-log space.

References

Run BAO filter.

Parameters

pk_interpolator (PowerSpectrumInterpolator1D, PowerSpectrumInterpolator2D) – Input power spectrum to remove BAO wiggles from.
degree (int, default=13) – Polynomial degree.
sigma (float, default=1) – Standard deviation of the Gaussian kernel that downweights the maximum of the power spectrum relative to the edges.
weight (float, default=0.5) – Normalisation of the Gaussian kernel.

compute()¶: Run filter.

property cosmo¶: Cosmology.

rs_drag_ratio()¶: If cosmo is provided, return the ratio of its rs_drag to the fiducial one (from Cosmology()), else 1.

set_k(nk=1024)¶

Set wavenumbers where to evaluate the power spectrum (between pk_interpolator.extrap_kmin and pk_interpolator.extrap_kmax).

Parameters: nk (int, default=1024) – Number of wavenumbers.

smooth_pk_interpolator(**kwargs)¶

Return smooth (i.e. no-wiggle) power spectrum.

Parameters: kwargs (dict) – Override interpolation and extrapolation settings of pk_interpolator.
Returns: interp – 1D or 2D depending on pk_interpolator.
Return type: PowerSpectrumInterpolator1D, PowerSpectrumInterpolator2D

smooth_xi_interpolator(**kwargs)¶

Return smooth (i.e. no-peak) correlation function using FFTlog.

Parameters: kwargs (dict) – Override interpolation and extrapolation settings of returned correlation function interpolator.
Returns: interp – 1D or 2D depending on pk_interpolator.
Return type: CorrelationFunctionInterpolator1D, CorrelationFunctionInterpolator2D

property wiggles¶: Extracted wiggles.

class cosmoprimo.bao_filter.Kirkby2013CorrelationFunctionBAOFilter(xi_interpolator, sbox_left=(50.0, 82.0), sbox_right=(150.0, 190.0), rescale_sbox=True, cosmo=None, **kwargs)¶

Bases: cosmoprimo.bao_filter.BaseCorrelationFunctionBAOFilter

Filter BAO peak by cutting the peak and interpolating with 5-order polynomial.

References

https://arxiv.org/abs/1301.3456 https://github.com/igmhub/picca/blob/master/bin/picca_compute_pk_pksb.py

Run BAO filter.

Parameters

xi_interpolator (CorrelationFunctionInterpolator1D, CorrelationFunctionInterpolator2D) – Input correlation function to remove BAO peak from.
sbox_left (tuple) – s-range to fit the polynomial on the left-hand side of the BAO peak.
sbox_right (tuple) – s-range to fit the polynomial on the right-hand side of the BAO peak.
cosmo (Cosmology) – Cosmology instance, which may be used to tune filter settings (depending on rs_drag).
rescale_sbox (bool) – Whether to rescale sbox_left and sbox_right by the ratio of rs_drag relative to the fiducial cosmology (may help robustify the procedure for cosmologies far from the fiducial one).
cosmo – Cosmology instance, used to compute the Eisenstein & Hu no-wiggle power spectrum.
kwargs (dict) – Arguments for set_s().

compute()¶: Run filter.

property cosmo¶: Cosmology.

rs_drag_ratio()¶: If cosmo is provided, return the ratio of its rs_drag to the fiducial one (from Cosmology()), else 1.

set_s(ns=1024)¶

Set separations where to evaluate the correlation function (between xi_interpolator.extrap_smin and xi_interpolator.extrap_smax).

Parameters: ns (int, default=1024) – Number of separations.

smooth_pk_interpolator(**kwargs)¶

Return smooth (i.e. no-wiggle) power spectrum using FFTlog.

Parameters: kwargs (dict) – Override interpolation and extrapolation settings of return power spectrum interpolator.
Returns: interp – 1D or 2D depending on pk_interpolator.
Return type: PowerSpectrumInterpolator1D, PowerSpectrumInterpolator2D

smooth_xi_interpolator(**kwargs)¶

Return smooth (i.e. no-peak) correlation function.

Parameters: kwargs (dict) – Override interpolation settings of xi_interpolator.
Returns: interp – 1D or 2D depending on xi_interpolator.
Return type: CorrelationFunctionInterpolator1D, CorrelationFunctionInterpolator2D

cosmoprimo.bao_filter.PowerSpectrumBAOFilter(pk_interpolator, engine='wallish2018', **kwargs)¶: Run power spectrum BAO filter corresponding to the provided engine.

class cosmoprimo.bao_filter.RegisteredCorrelationFunctionBAOFilter(name, bases, class_dict)¶

Bases: type

Metaclass registering BaseCorrelationFunctionBAOFilter-derived classes.

mro()¶: Return a type’s method resolution order.

class cosmoprimo.bao_filter.RegisteredPowerSpectrumBAOFilter(name, bases, class_dict)¶

Bases: type

Metaclass registering BasePowerSpectrumBAOFilter-derived classes.

mro()¶: Return a type’s method resolution order.

class cosmoprimo.bao_filter.SavGolPowerSpectrumBAOFilter(pk_interpolator, cosmo=None, **kwargs)¶

Bases: cosmoprimo.bao_filter.BasePowerSpectrumBAOFilter

BAO smoothing with Savitzky-Golay filter.

References

Taken from https://github.com/sfschen/velocileptors/blob/master/velocileptors/EPT/ept_fullresum_fftw.py

Note

Contrary to the reference, we work in \(\log(k)\) - \(\log(k P(k))\) space.

Run BAO filter.

Parameters

pk_interpolator (PowerSpectrumInterpolator1D, PowerSpectrumInterpolator2D) – Input power spectrum to remove BAO wiggles from.
cosmo (Cosmology, default=None) – Cosmology instance, which may be used to tune filter settings (depending on rs_drag).
kwargs (dict) – Arguments for set_k().

compute()¶: Run filter.

property cosmo¶: Cosmology.

rs_drag_ratio()¶: If cosmo is provided, return the ratio of its rs_drag to the fiducial one (from Cosmology()), else 1.

set_k(nk=1024)¶

Set wavenumbers where to evaluate the power spectrum (between pk_interpolator.extrap_kmin and pk_interpolator.extrap_kmax).

Parameters: nk (int, default=1024) – Number of wavenumbers.

smooth_pk_interpolator(**kwargs)¶

Return smooth (i.e. no-wiggle) power spectrum.

Parameters: kwargs (dict) – Override interpolation and extrapolation settings of pk_interpolator.
Returns: interp – 1D or 2D depending on pk_interpolator.
Return type: PowerSpectrumInterpolator1D, PowerSpectrumInterpolator2D

smooth_xi_interpolator(**kwargs)¶

Return smooth (i.e. no-peak) correlation function using FFTlog.

Parameters: kwargs (dict) – Override interpolation and extrapolation settings of returned correlation function interpolator.
Returns: interp – 1D or 2D depending on pk_interpolator.
Return type: CorrelationFunctionInterpolator1D, CorrelationFunctionInterpolator2D

property wiggles¶: Extracted wiggles.

class cosmoprimo.bao_filter.Wallish2018PowerSpectrumBAOFilter(pk_interpolator, cosmo=None, **kwargs)¶

Bases: cosmoprimo.bao_filter.BasePowerSpectrumBAOFilter

Filter BAO wiggles by sine-transforming the power spectrum to real space (where the BAO is better localised), cutting the peak and interpolating with a spline.

References

https://arxiv.org/pdf/1810.02800.pdf, Appendix D (thanks to Stephen Chen for the reference)

Note

We have hand-tune parameters w.r.t. to the reference.

Run BAO filter.

Parameters

pk_interpolator (PowerSpectrumInterpolator1D, PowerSpectrumInterpolator2D) – Input power spectrum to remove BAO wiggles from.
cosmo (Cosmology, default=None) – Cosmology instance, which may be used to tune filter settings (depending on rs_drag).
kwargs (dict) – Arguments for set_k().

compute()¶: Run filter.

property cosmo¶: Cosmology.

rs_drag_ratio()¶: If cosmo is provided, return the ratio of its rs_drag to the fiducial one (from Cosmology()), else 1.

set_k(nk=1024)¶

Set wavenumbers where to evaluate the power spectrum (between pk_interpolator.extrap_kmin and pk_interpolator.extrap_kmax).

Parameters: nk (int, default=1024) – Number of wavenumbers.

smooth_pk_interpolator(**kwargs)¶

Return smooth (i.e. no-wiggle) power spectrum.

Parameters: kwargs (dict) – Override interpolation and extrapolation settings of pk_interpolator.
Returns: interp – 1D or 2D depending on pk_interpolator.
Return type: PowerSpectrumInterpolator1D, PowerSpectrumInterpolator2D

smooth_xi_interpolator(**kwargs)¶

Return smooth (i.e. no-peak) correlation function using FFTlog.

Parameters: kwargs (dict) – Override interpolation and extrapolation settings of returned correlation function interpolator.
Returns: interp – 1D or 2D depending on pk_interpolator.
Return type: CorrelationFunctionInterpolator1D, CorrelationFunctionInterpolator2D

property wiggles¶: Extracted wiggles.

FFTlog¶

Implementation of the FFTlog algorithm, very much inspired by mcfit (https://github.com/eelregit/mcfit) and implementation in https://github.com/sfschen/velocileptors/blob/master/velocileptors/Utils/spherical_bessel_transform_fftw.py

class cosmoprimo.fftlog.BaseBesselKernel(nu)¶

Base Bessel kernel.

class cosmoprimo.fftlog.BaseFFTEngine(size, nparallel=1, nthreads=None)¶

Bases: object

Base FFT engine.

Initialize FFT engine.

Parameters

size (int) – Array size.
nparallel (int, default=1) – Number of FFTs to be performed in parallel.
nthreads (int, default=None) – Number of threads.

class cosmoprimo.fftlog.BaseKernel¶

Bases: object

Base kernel.

class cosmoprimo.fftlog.BaseTophatKernel(ndim=1)¶

Base tophat kernel.

class cosmoprimo.fftlog.BesselJKernel(nu)¶

Bases: cosmoprimo.fftlog.BaseBesselKernel

(Mellin transform of) Bessel kernel.

class cosmoprimo.fftlog.CorrelationToPower(s, ell=0, q=0, complex=False, **kwargs)¶

Correlation function to power spectrum transform, defined as:

\[P_{\ell}(k) = 4 \pi i^{\ell} \int ds s^{2} \xi_{\ell}(s) j_{\ell}(ks)\]

Initialize power to correlation transform.

Parameters

s (array_like) – Input log-spaced separations. If 1D, is broadcast to the number of provided ell.
ell (int, list of int, default=0) – Poles. If a list is provided, will perform all transforms at once.
q (float, list of floats, default=0) – Power-law tilt(s) to regularise integration.
complex (bool, default=False) – False returns the real part of even poles, and the imaginary part of odd poles.
kwargs (dict) – Arguments for FFTlog.

inv()¶: Inverse the transform.

property nparallel¶: Number of transforms performed in parallel.

set_fft_engine(engine='numpy', **engine_kwargs)¶

Set up FFT engine. See get_fft_engine()

Parameters

engine (BaseEngine, string, default='numpy') – FFT engine, or one of [‘numpy’, ‘fftw’].
engine_kwargs (dict) – Arguments for FFT engine.

setup()¶: Set up u funtions.

class cosmoprimo.fftlog.FFTWEngine(size, nparallel=1, nthreads=None, wisdom=None, plan='measure')¶

Bases: cosmoprimo.fftlog.BaseFFTEngine

FFT engine based on pyfftw.

Initialize pyfftw engine.

Parameters

size (int) – Array size.
nparallel (int, default=1) – Number of FFTs to be performed in parallel.
nthreads (int, default=None) – Number of threads.
wisdom (string, tuple, default=None) – pyfftw wisdom, to speed up initialization of FFTs. If a string, should be a path to the save FFT wisdom (with numpy.save()). If a tuple, directly corresponds to the wisdom.
plan (string, default='measure') – Choices are [‘estimate’, ‘measure’, ‘patient’, ‘exhaustive’]. The increasing amount of effort spent during the planning stage to create the fastest possible transform. Usually ‘measure’ is a good compromise.

backward(fun)¶: Backward transform of fun.

forward(fun)¶: Forward transform of fun.

class cosmoprimo.fftlog.FFTlog(x, kernel, q=0, minfolds=2, lowring=True, xy=1, check_level=0, engine='numpy', **engine_kwargs)¶

Bases: object

Implementation of the FFTlog algorithm presented in https://jila.colorado.edu/~ajsh/FFTLog/, which computes the generic integral:

\[G(y) = \int_{0}^{\infty} x dx F(x) K(xy)\]

with \(F(x)\) input function, \(K(xy)\) a kernel.

This transform is (mathematically) invariant under a power law transformation:

\[G_{q}(y) = \int_{0}^{\infty} x dx F_{q}(x) K_{q}(xy)\]

where \(F_{q}(x) = G(x)x^{-q}\), \(K_{q}(t) = K(t)t^{q}\) and \(G_{q}(y) = G(y)y^{q}\).

Initialize FFTlog, which can perform several transforms at once.

Parameters

x (array_like) – Input log-spaced coordinates. Must be strictly increasing. If 1D, is broadcast to the number of provided kernels.
kernel (callable, list of callables) – Mellin transform of the kernel: .. math:: U_{K}(z) = int_{0}^{infty} t^{z-1} K(t) dt If a list of kernels is provided, will perform all transforms at once.
q (float, list of floats, default=0) – Power-law tilt(s) to regularise integration.
minfolds (int, default=2) – The c is chosen with minimum \(n\) chosen such that 2**n > minfolds * x.size.
lowring (bool, default=True) – If True set output coordinates according to the low-ringing condition, otherwise set it with xy.
xy (float, list of floats, default=1) – Enforce the reciprocal product (i.e. x[0] * y[-1]) of the input x and output y coordinates.
check_level (int, default=0) – If non-zero run sanity checks on input.
engine (string, default='numpy') – FFT engine. See set_fft_engine().
engine_kwargs (dict) – Arguments for FFT engine.

Note

Kernel definition is different from that of https://jila.colorado.edu/~ajsh/FFTLog/, which uses (eq. 10):

\[U_{K}(z) = \int_{0}^{\infty} t^{z} K(t) dt\]

Therefore, one should use \(q = 1\) for Bessel functions to match \(q = 0\) in https://jila.colorado.edu/~ajsh/FFTLog/.

inv()¶: Inverse the transform.

property nparallel¶: Number of transforms performed in parallel.

set_fft_engine(engine='numpy', **engine_kwargs)¶

Set up FFT engine. See get_fft_engine()

Parameters

engine (BaseEngine, string, default='numpy') – FFT engine, or one of [‘numpy’, ‘fftw’].
engine_kwargs (dict) – Arguments for FFT engine.

setup()¶: Set up u funtions.

class cosmoprimo.fftlog.GaussianKernel¶

(Mellin transform of) Gaussian kernel.

class cosmoprimo.fftlog.GaussianSqKernel¶

(Mellin transform of) square of Gaussian kernel.

class cosmoprimo.fftlog.GaussianVariance(k, q=0, **kwargs)¶

Variance in Gaussian window.

It relies on Gaussian kernel.

Initialize Gaussian variance transform.

Parameters

k (array_like) – Input log-spaced wavenumbers. If 1D, is broadcast to the number of provided ell.
q (float, list of floats, default=0) – Power-law tilt(s) to regularise integration.
kwargs (dict) – Arguments for FFTlog.

inv()¶: Inverse the transform.

property nparallel¶: Number of transforms performed in parallel.

set_fft_engine(engine='numpy', **engine_kwargs)¶

Set up FFT engine. See get_fft_engine()

Parameters

engine (BaseEngine, string, default='numpy') – FFT engine, or one of [‘numpy’, ‘fftw’].
engine_kwargs (dict) – Arguments for FFT engine.

setup()¶: Set up u funtions.

class cosmoprimo.fftlog.HankelTransform(x, nu=0, **kwargs)¶

Hankel transform implementation using FFTlog.

It relies on Bessel function kernels.

Initialize Hankel transform.

Parameters

x (array_like) – Input log-spaced coordinates. If 1D, is broadcast to the number of provided nu.
nu (int, list of int, default=0) – Order of Bessel functions. If a list is provided, will perform all transforms at once.
kwargs (dict) – Arguments for FFTlog.

inv()¶: Inverse the transform.

property nparallel¶: Number of transforms performed in parallel.

set_fft_engine(engine='numpy', **engine_kwargs)¶

Set up FFT engine. See get_fft_engine()

Parameters

engine (BaseEngine, string, default='numpy') – FFT engine, or one of [‘numpy’, ‘fftw’].
engine_kwargs (dict) – Arguments for FFT engine.

setup()¶: Set up u funtions.

class cosmoprimo.fftlog.NumpyFFTEngine(size, nparallel=1, nthreads=None)¶

Bases: cosmoprimo.fftlog.BaseFFTEngine

FFT engine based on numpy.fft.

Initialize FFT engine.

Parameters

size (int) – Array size.
nparallel (int, default=1) – Number of FFTs to be performed in parallel.
nthreads (int, default=None) – Number of threads.

backward(fun)¶: Backward transform of fun.

forward(fun)¶: Forward transform of fun.

class cosmoprimo.fftlog.PowerToCorrelation(k, ell=0, q=0, complex=False, **kwargs)¶

Power spectrum to correlation function transform, defined as:

\[\xi_{\ell}(s) = \frac{(-i)^{\ell}}{2 \pi^{2}} \int dk k^{2} P_{\ell}(k) j_{\ell}(ks)\]

Initialize power to correlation transform.

Parameters

k (array_like) – Input log-spaced wavenumbers. If 1D, is broadcast to the number of provided ell.
ell (int, list of int, default=0) – Poles. If a list is provided, will perform all transforms at once.
q (float, list of floats, default=0) – Power-law tilt(s) to regularise integration.
complex (bool, default=False) – False assumes the imaginary part of odd power spectrum poles is provided.
kwargs (dict) – Arguments for FFTlog.

inv()¶: Inverse the transform.

property nparallel¶: Number of transforms performed in parallel.

set_fft_engine(engine='numpy', **engine_kwargs)¶

Set up FFT engine. See get_fft_engine()

Parameters

engine (BaseEngine, string, default='numpy') – FFT engine, or one of [‘numpy’, ‘fftw’].
engine_kwargs (dict) – Arguments for FFT engine.

setup()¶: Set up u funtions.

class cosmoprimo.fftlog.SphericalBesselJKernel(nu)¶

Bases: cosmoprimo.fftlog.BaseBesselKernel

(Mellin transform of) spherical Bessel kernel.

class cosmoprimo.fftlog.TophatKernel(ndim=1)¶

Bases: cosmoprimo.fftlog.BaseTophatKernel

(Mellin transform of) tophat kernel.

class cosmoprimo.fftlog.TophatSqKernel(ndim=1)¶

Bases: cosmoprimo.fftlog.BaseTophatKernel

(Mellin transform of) square of tophat kernel.

class cosmoprimo.fftlog.TophatVariance(k, q=0, **kwargs)¶