NumCosmo – 1.0

CLASS (Cosmic Linear Anisotropy Solving System) backend.

CLASS (Cosmic Linear Anisotropy Solving System) backend for perturbations.

Cluster abundance distribution.

Abstract class for cluster mass distributions.

Cluster mass-richness distribution model based on Ascaso et al.

Sunyaev-Zel’dovich cluster mass distribution.

Sunyaev-Zel’dovich and x-ray cluster abundance mass distribution.

Extended cluster mass-richness distribution model.

Cluster mass ln-normal distribution.

Cluster mass real mass distribution.

Planck-CLASH Cluster Mass Distribution.

Abstract class for cluster mass-richness observable relations.

Cluster mass distribution model based on Selection et al.

Sunyaev-Zel’dovich cluster mass distribution.

Individual gaussian photometric distribution for clusters.

Global gaussian photometric distribution for clusters.

Model for the pseudo number counts of galaxy clusters.

Abstract class for cluster redshift distributions.

Cluster abundance redshift real redshift distribution.

Cluster and CMB lensing correlation using halo model and Limber approximation.

Baryon oscillation data — acoustic scale $A$.

Baryon Oscillation Data — $(D_H/r,\; D_A/r)$ data.

Baryon Oscillation Data — $(D_M/r,\; H/r)$ data.

Baryon Oscillation Data — $(D_H/r,\; D_t/r)$ data.

Baryon oscillation data — volume mean $D_V$.

Baryon oscillation data — $D_V / D_V$ ratio.

Baryon oscillation data — $D_V / r_s$ empirical likelihood.

Baryon oscillation data — $D_H / r_d$ and $D_t / r_d$ empirical likelihood.

Baryon Oscillation Data — $r_s / D_V$ ratio.

Cluster mass richness data object.

Cluster mass-richness data object using true (integer) richness counts.

Cluster number count data.

Cluster number count data gaussian likelihood.

Galaxy clusters data — pseudo number counts likelihood.

Cluster weak-lensing likelihood built on the per-galaxy Factor calculators (NcGalaxyPositionFactor / NcGalaxyRedshiftFactor / NcGalaxyShapeFactor).

Cosmic microwave background data — distance priors.

Cosmic microwave background data — shift parameter.

Likelihood object for distance modulus data.

Hubble function data.

Hubble function data from BAO.

Planck Likelihood interface.

Type Ia supernovae data with covariance error matrix.

Cross-correlation data object.

Dark energy contraction perturbations model.

Cosmological distance and time related quantities.

Galaxy angular correlation function.

Abstract halo occupation distribution.

Zheng et al. (2007) halo occupation distribution.

Abstract calculator for the galaxy sky-position distribution.

Flat (uniform) galaxy sky-position scheme.

Binning calculator: the true-redshift distribution of a photometric bin.

Abstract calculator for the galaxy joint redshift distribution.

Composed redshift calculator scheme: a population convolved with an observable.

Spline redshift calculator scheme: a per-galaxy pre-tabulated $p(z)$.

Abstract model for the photometric-redshift observable model $P(\mathrm{data}|z)$.

Gaussian photometric-redshift observable model.

Abstract population-level photo-z observable distribution.

Gaussian population photo-z observable distribution.

Class describing galaxy sample redshift distributions.

Class describing galaxy sample redshift distributions as in LSST-SRD.

Galaxy phenomelogical selection function.

Shape likelihood-factor calculator for the weak-lensing pipeline.

CGF-expansion evaluation of the intrinsic-ellipticity marginal.

Fixed-node lens-domain quadrature evaluation of the intrinsic-ellipticity marginal.

Laplace-approximate evaluation of the intrinsic-ellipticity marginal.

Exact quadrature evaluation of the intrinsic-ellipticity marginal.

Lensed-frame series evaluation of the intrinsic-ellipticity marginal, both ellipticity conventions, arbitrary truncation order, any population model implementing NcGalaxyShapePop‘s eval_p_rho2_g_series vfunc (currently NcGalaxyShapePopGauss, NcGalaxyShapePopGaussLocal and NcGalaxyShapePopBeta).

Variance-add evaluation of the intrinsic-ellipticity marginal.

Abstract model for the intrinsic galaxy ellipticity distribution.

Beta intrinsic ellipticity distribution (BetaGlobal).

Truncated-Gaussian intrinsic ellipticity distribution.

Truncated-Gaussian intrinsic ellipticity distribution, per-galaxy width.

Galaxy weak lensing observation data.

Growth function of linear perturbations.

Abstract class for halo bias function type.

Despali halo bias function type.

Press-Schechter halo bias function type.

Sheth-Tormen elliptical halo bias function type.

Sheth-Tormen spherical halo bias function type.

Tinker halo bias function type.

Catalog of halos, clusters or member objects.

Samples a NcHaloCatalog from a cluster abundance model.

Populates a host NcHaloCatalog with member galaxies through a NcGalaxyHOD.

Class defining the Bhattacharya et al. 2013 concentration-mass relation.

Class defining the Diemer & Kravtsov (2015) concentration-mass relation Diemer and Kravtsov (2015).

Class defining the Duffy et al. 2008 concentration-mass relation. The concentration parameter $c_\Delta$ is given by: $$c_\Delta = A \left(\frac{M_\Delta}{M_\mathrm{pivot}}\right)^B (1+z)^C,$$ where $M_\mathrm{pivot} = 2 \times 10^{12} h^{-1} M_\odot$ and the parameters $(A, B, C)$ depend on the mass definition (mean, critical, or virial).

Class defining the Dutton et al. 2014 concentration-mass relation.

Class defining the Klypin et al. (2011) concentration-mass relation Klypin et al. (2011).

Class defining mass and concentration as parameters.

Class defining the Prada et al. 2012 concentration-mass relation.

Abstract class for spherical halo density profiles.

Density profile of Diemer \& Kravtsov type.

Einasto density profile.

Hernquist density profile.

Navarro-Frenk-White (NFW) density profile.

Clusters mass function.

Class describing halo mass summary.

A class to represent the center of a halo.

Abstract class for implementing homogeneous and isotropic cosmological models.

Base class for implementing dark energy models.

Dark Energy — Chevallier–Polarski–Linder equation of state.

Dark Energy — Jassal-Bagla-Padmanabhan equation of state.

Dark Energy — CMB reparametrization.

Dark Energy — reparametrization $\Omega_{x0} \to \Omega_{k0}$.

Dark Energy — spline equation of state.

Dark Energy — constant equation of state.

Generalized Chaplygin Gas.

Interacting Dark Energy Model.

$\Lambda$CDM model.

Kinetic model — Constant deceleration function.

Radiation plus $w$-fluid model with a quantum generated bounce phase model.

The $w$-fluid model with a quantum generated bounce phase model.

Kinetic model — Linear deceleration function.

Kinetic model — Radial basis function deceleration function.

Kinetic model — Spline deceleration function.

Single scalar field with an exponential potential.

Base class for perturbation in homogeneous and isotropic cosmologies.

Perturbation object for adiabatic mode only.

Perturbation background variables transport object.

Base class for perturbative Boltzmann hierarchy.

CLASS (Cosmic Linear Anisotropy Solving System) backend for perturbations.

Perturbations object for standard Boltzmann hierarchy model.

Base class describing a general perturbation component.

Photon-Baryon plasma compoment.

Perturbation object for electromagnetic mode.

Base class for implementing first order perturbation in a Friedmann background.

Base class describing a general first order gravitation theory.

First order Einstein equations on a Friedmann background.

Perturbation object for gravitational wave mode.

Perturbation object for a two fluids system.

Abstract class for implementing homogeneous and isotropic primordial cosmological models.

Arctangent modification of the power law primordial spectrum.

Broken power law modification of the power law primordial spectrum.

Exponential cutoff modification of the power law primordial spectrum.

Power law implementation for primordial spectra.

Smooth Broken power law modification of the power law primordial spectrum.

Two Fluids implementation for primordial spectra.

Minisuperspace 1D quantum gravity models.

Abstract class for implementing homogeneous and isotropic reionization models.

CAMB-like reionization object.

CAMB reionization reparametrization $z_\mathrm{reion} \to \tau_\mathrm{reion}$.

Dark matter halo multiplicity function.

Dark matter halo — Bhattacharya multiplicity function.

Dark matter halo — Bocquet multiplicity function.

Dark matter halo — Crocce multiplicity function.

Dark matter halo — Despali multiplicity function.

Dark matter halo — Jenkins multiplicity function.

Dark matter halo — Press-Schechter multiplicity function.

Dark matter halo — Sheth-Tormen multiplicity function.

Dark matter halo — Tinker multiplicity function.

Dark matter halo — Tinker normalized multiplicity function mean matter density.

Dark matter halo — Warren multiplicity function.

Dark matter halo — Watson multiplicity function.

Abstract class for Planck Foreground and Instrument models.

Planck Foreground and Instrument model for TT correlation maps.

Planck Foreground and Instrument model for TT correlation maps.

Abstract class for linear matter power spectrum implementation.

Linear matter power spectrum from CLASS backend.

Class for linear matter power spectrum from a 1d-spline.

Class for linear matter power spectrum from a transfer function.

Abstrac class for non-linear matter power spectrum implementation.

Nonlinear matter power spectrum from Halofit model.

Abstract class for cosmic recombination.

Cosmic recombination by Class.

Cosmic recombination implementing Seager (1999).

Reduced Shear Calibration.

Reduced Shear Calibration.

Cluster mass estimation via reduced shear observable.

Scale factor as a function of the conformal time.

Supernovae distance covariance between distance estimates.

Abstrac class for perturbation transfer function.

Bardeen, Bond, Kaiser and Szalay (BBKS) transfer function.

Transfer function using CAMB as backend.

Eisenstein-Hu fitting function for the transfer function.

Eisenstein-Hu fitting function for the transfer function with no baryons.

Abstract class for window functions.

A gaussian window function.

A top-hat window function.

Truncated $g$-Taylor series of nc_wl_ellipticity.h’s own closed-form reduced-shear kernels: $\chi_I(\chi_L,g)$ (via apply_shear_inv) and the linear (not log) Jacobian $\mathrm{Jac}(\chi_L,g)=|\det J|$ (via det_jac), one object per ellipticity convention, mirroring that file’s own _trace/_trace_det split.

Weak lensing surface mass density.

Cross-correlations data storage object.

Base object for the kernels of projected observables used in cross-correlations.

Base class for cluster kernels in cross-correlations.

Implementation of cluster kernel using a top-hat redshift distribution.

Implementation of NcXcorKernel for integrated Sachs-Wolfe (ISW).

Implementation of NcXcorKernel for CMB lensing.

Abstract base class for kernel components in cross-correlation calculations.

Implementation of NcXcorKernel for galaxy density.

Thermal Sunyaev Zel’dovich effect kernel.

Implementation of NcXcorKernel for galaxy weak lensing.

Abstract class for computing lensing efficiency.

Perturbation interface for two fluids system.

Per-galaxy data for the photometric-redshift observable model. Following the NcGalaxyShapePopData idiom, the whole per-galaxy photometric-redshift observation (e.g. the point estimate and its scatter) lives in the opaque ldata owned by the concrete subclass: the observation’s structure is defined by the observable model, so the redshift calculator never accesses it directly.

Per-galaxy data for the intrinsic ellipticity distribution. Mirrors the NcGalaxyShapeFactorData / NcGalaxyPositionFactorData idiom: typed public fields plus an opaque ldata holding the subclass-specific, varying/updatable resolved parameters (filled by nc_galaxy_shape_pop_prepare()). The model is the factory (nc_galaxy_shape_pop_data_new()).

Boxed object containing the current status of the ode system.

Gravitation section info.

Boxed object describing scalar modes of the gravitational perturbations.

Boxed object describing tensor modes of the gravitational perturbations.

Boxed object describing scalar modes of the energy-momentum tensor perturbations.

Boxed object describing the dependencies of the scalar modes of the gravitational perturbations.

Boxed object describing tensor modes of the energy-momentum tensor perturbations.

Boxed object describing vector modes of the energy-momentum tensor perturbations.

Boxed object describing vector modes of the gravitational perturbations.

Structure used to store the perturbations’ equations of motion coefficients for the two-fluid model.

Structure used to store the perturbations’ state for the two-fluid model.

Structure used to store the perturbations’ transfer functions for the two-fluid model.

Structure representing the WKB approximations of perturbations in the two-fluid model. Stores two approximations, one for each eigenmode, along with their corresponding estimated WKB scales.

Exponential wave-function.

Gaussian wave-function.

Semi-Quantum approximation fiducial wave-function.

Cache for the critical surface mass density.

Lens-side context that caches the z_lens-dependent constants shared across many source redshifts during crit_cache_prep.

Optimization structure.

Cache for the surface mass density.

A reference-counted closure for computing kernel integrands. The eval_func function should fill len values in the W array for the given wavenumber k.

A boxed type for the kinetic quantities necessary to compute the kernels.

Parameters for the Ascaso cluster mass-richness relation.

Parameters for the Benson cluster mass-SZ relation.

Parameters for the Benson cluster mass-X-ray relation.

Parameters for the extended cluster mass-richness relation.

Parameters for the log-normal cluster mass-observable relation.

Parameters for the Planck cluster mass relation combining SZ and lensing.

Scalar parameters for the cluster mass-richness relation.

Cluster mass selection function model parameters.

Parameters for the Vanderlinde cluster mass-SZ relation.

Parameters for the global Gaussian photometric redshift distribution.

Cluster pseudo counts model parameters.

Enumeration of available BAO (Baryon Acoustic Oscillations) datasets.

Cluster abundance data input modes. These specify how the cluster number count data is initialized or used.

Wilkinson Microwave Anisotropy Probe (WMAP) distance priors and shift parameter estimates.

Available BAO samples for Hubble function measurements. These identifiers select specific datasets for the Hubble parameter derived from Baryon Acoustic Oscillation observations.

Identifiers for different Hubble parameter observational datasets.

The Planck likelihood types.

Data ordering for covariance.

Strategy used by NcDataSNIACov to resample a mock realization. Not every dataset ships the light-curve covariance, so NC_DATA_SNIA_COV_RESAMPLE_FROM_LIGHTCURVE is only valid when nc_data_snia_cov_has_complete_cov() is TRUE.

Supernovae data sets.

Enumeration to define which method to be applied in order to compute the cosmological distances.

Zheng et al. (2007) HOD parameters.

Gaussian population photo-z observable model parameters.

LSST SRD galaxy redshift distribution model parameters.

LSST SRD galaxy redshift distribution types.

Beta intrinsic ellipticity model parameters, with $\alpha = \mu\nu$ and $\beta = (1-\mu)\nu$.

Truncated-Gaussian intrinsic ellipticity model parameters.

Method used to compute the ellipticity from the quadrupole moment matrix. The quadrupole matrix can be normalized either by its trace or by a combination of trace and determinant. In both cases, the shape can be described by an ellipse parameterized as $$ \left(\frac{x\cos\theta + y\sin\theta}{a}\right)^2 + \left(\frac{y\cos\theta - x\sin\theta}{b}\right)^2 = 1, $$ where $a$ and $b$ are the semi-major and semi-minor axes, and $\theta$ is the orientation angle.

The kind of objects stored in a NcHaloCatalog. It is schema metadata only: all kinds share the same generic column storage; the linkage between catalogs is expressed through the id and parent-id columns.

Fundamental parametrization of the profile $\rho(r)$. The halo mass is a paremeter while the concentration is given by the Bhattacharya et al. (2013) concentration-mass relation.

Fundamental parametrization of the profile $\rho(r)$. The halo mass is a paremeter while the concentration is given by the Diemer & Kravtsov (2015) concentration-mass relation.

Fundamental parametrization of the profile $\rho(r)$. The halo mass is a paremeter while the concentration is given by the Duffy et al. (2008) concentration-mass relation.

Fundamental parametrization of the profile $\rho(r)$. The halo mass is a paremeter while the concentration is given by the Dutton & Macciò (2014) concentration-mass relation.

Fundamental parametrization of the profile $\rho(r)$. The halo mass is a paremeter while the concentration is given by the Klypin et al. (2011) concentration-mass relation.

Fundamental parametrization of the profile $\rho(r)$. Both mass and concentration are parameters.

Fundamental parametrization of the profile $\rho(r)$. The halo mass is a paremeter while the concentration is given by the Prada et al. (2012) concentration-mass relation.

Methods for parametrizing the DK14 halo density profile.

The first three parameters, $\rho_s$, $r_s$ and $\alpha$, are the Einasto profile’s parameters. The transition term $f_{trans}$ is a function parametrized by $r_t$, $beta$ and $\gamma$. These two functions determine the inner profile, whereas the outer profile is parametrized br $b_e$ and $s_e$.

Parameters for the Einasto halo density profile.

Options for optimizing spline interpolation in halo mass function calculations.

Spherical overdensity halo mass: $$M_\Delta = \frac{4\pi}{3} \Delta \rho_\mathrm{bg} r_\Delta^3,$$ where $\rho_\mathrm{bg}$ is the background density of the universe at redshift z, $\rho_\mathrm{bg} (z)$. For NC_HALO_MASS_SUMMARY_MASS_DEF_VIRIAL the virial overdensity is defined as: \begin{equation}\label{def:DVir} \Delta_\mathrm{Vir} = 18 \pi^2 + 82 x - 39 x^2, \quad x \equiv \Omega_m(z) - 1. \end{equation}.

Halo center model parameters.

Dark Energy equation of state: $w(z) = w_0 + w_1 \frac{z}{1.0 + z}$.

Dark Energy equation of state: $w(z) = w_0 + w_1 \frac{z}{(1.0 + z)^2}$.

Scalar parameters for dark energy cosmological models. These are the standard cosmological parameters extended to include dark energy contributions.

Vector parameters for dark energy cosmological models. These arrays specify properties of massive neutrino species, allowing for multiple neutrino families with different masses and temperatures.

Dark Energy equation of state: $w(z) = w$.

Scalar parameters for the generalized Chaplygin gas cosmological model.

Vector parameters for massive neutrinos in the generalized Chaplygin gas model.

Scalar parameters for interacting dark energy-matter cosmology models (IDEM2).

Vector parameters for interacting dark energy-matter cosmology models (IDEM2).

Parameter of the Quantum Gravity Radiation W model.

Parameter of the Quantum Gravity Radiation W model.

Scalar parameters for Q-spline cosmological model. This parametrization uses splines for the deceleration parameter q(z).

Vector parameters for Q-spline cosmological model. The deceleration parameter spline knots define the evolution of $q(z)$.

Knot placement for the spline-based $w(z)$ / $q(z)$ reconstruction models (NcHICosmoDEWSpline, NcHICosmoQSpline). Uniform spreads resolution evenly; Chebyshev clusters it toward the endpoints (better interpolation conditioning, but denser where high-$z$ data are sparse).

Electromagnetic coupling enumerator.

Scalar field parameters enumerator. This enumerator is used to access the scalar field parameters in the NcHICosmoVexp object.

Perturbation variables enumerator.

Variables for the Boltzmann perturbation equations.

Photon-baryon component variables.

Perturbation variables enumerator.

ODE integrators.

Gravitation gauges.

Elements present in the scalar equations.

Perturbation variables enumerator.

Enumeration of physical observables computed from the two-fluid perturbation state.

Specifies which quantized mode(s) to include when computing two-point observables such as power spectra and correlations.

Enumeration of variables used in the two-fluid model.

Error domain for NcHIPertTwoFluids.

Primordial adiabatic scalar power spectrum: $$ \mathcal{P}{SA}(k) = \xi\mathrm{neq}(k)\mathcal{P}{\mathrm{F}}(k),$$ where $$ \mathcal{P}{\mathrm{F}}(k) \equiv \mathcal{A}\mathrm{s}\left(\frac{k}{k\star}\right)^{n_s -1 } $$ and $$ \xi_\mathrm{neq}(k) = \arctan \left[ \left(\frac{k}{k_\mathrm{c}}\right)^\lambda + c_2\right] - \frac{\pi}{2} + c_3. $$.

Broken power-law primordial power spectrum parameters. These parameters define a primordial power spectrum with a break, useful for modeling features in the inflationary potential.

Parameters for the exponential cutoff primordial spectrum model.

Primordial adiabatic scalar power spectrum: $$ \mathcal{P}{SA}(k) = \mathcal{A}\mathrm{s}\left(\frac{k}{k_\star}\right)^{n_s -1 }.$$.

Parameters for the smooth broken power law primordial spectrum model.

Parameters for the two fluids primordial power spectrum.

CAMB-like reionization model parameters.

Selects the redshift evolution of the shape parameter $a$. The two papers state the same functional form with the same $z = 0$ parameters; they differ only in whether $a$ evolves with redshift. See arXiv:1005.2239 (Bhattacharya et al. 2011) and arXiv:1904.11970 (Heitmann et al. 2019).

Spherical overdensity halo mass: $$M_\Delta = \frac{4\pi}{3} \Delta \rho_\mathrm{bg} r_\Delta^3,$$ where $\rho_\mathrm{bg}$ is the background density of the universe at redshift z, $\rho_\mathrm{bg} (z)$. For NC_HALO_DENSITY_PROFILE_MASS_DEF_VIRIAL the virial overdensity is defined as: \begin{equation}\label{def:DVir} \Delta_\mathrm{Vir} = 18 \pi^2 + 82 x - 39 x^2, \quad x \equiv \Omega_m(z) - 1. \end{equation}.

Planck Foregound and Instrument parameters, compatible with 2013, 2015 and 2018 releases (see Planck 2015 results XI (2015) and Planck 2018 results V (2019)).

Planck Foregound and Instrument parameters, compatible with 2013, 2015 and 2018 releases (see Planck 2015 results XI (2015) and Planck 2018 results V (2019)).

WtG calibration parameters.

These parameters refers to the shear calibration, and the Voigt profile.

SN Ia distance covariance model parameters.

SN Ia distance covariance model parameters.

BBKS transfer function variant.

Handedness of the orthonormal frame whose basis vectors are used to resolve a complex spin-2 ellipticity (or reduced shear) into its two components.

Weak lensing surface mass density model parameters.

Scalar parameters for CMB lensing kernel (currently none defined).

Enum values for the tSZ kernel parameters.

Methods to compute integrals.

Each type corresponds to one CMB two-point correlation function data to be used: TT (temperature only), EE (E-mode only), BB (B-mode only), TE (temperature and E-mode polarization), TB (temperature and B-mode polarization), EB (E- and B-mode polarization) and $\phi\phi$ (CMB lensing). The last option `ALL’ selects all data listed above.

Implementation flags for dark energy models. These flags indicate which virtual methods are implemented by a specific dark energy model subclass.

Flags defining the implementation options of the NcHICosmo abstract object.

Methods to be implementd by every primordial model.

Options for the Seager recombination model.

NcDataSNIACov error messages.

Error codes returned by NcGalaxyShapeFactor methods.

Error codes returned by the NcHaloCatalog class.

Error codes returned by the NcHaloCatalogMemberGenerator class.

Wave-function.

Evaluates the kernel function K(k, xi) at the given comoving distance and wave number.

Evaluates the prefactor that may depend on k and ℓ.

Gets the valid integration ranges for this component.

Function type for evaluating kernel integrands.

Function type for getting the valid k range.

Evaluates the source weight function $W_{\mathrm{src}}(z)$ for the lensing efficiency computation. This is used in the integral: \begin{equation} g(z) = \int_z^{z_{\max}} dz’ \left(1 - \frac{\chi(z)}{\chi(z’)}\right) W_{\mathrm{src}}(z’) \end{equation}.

Returns the redshift range for the source distribution used in lensing efficiency computation.

Creates a NcmData for the given id.

Creates a new NcmData of type NcDataCMBId.

Recovers the intrinsic ellipticity e from the observed ellipticity e_obs under the reduced shear g, in the trace-determinant (ellipticity) convention.

Recovers the intrinsic distortion chi from the observed distortion chi_obs under the reduced shear g, in the trace (distortion) convention.

Applies the reduced shear g to the intrinsic ellipticity e in the trace-determinant (ellipticity) convention, storing the result in e_obs.

Applies the reduced shear g to the intrinsic distortion chi in the trace (distortion) convention, storing the result in chi_obs.

Computes the natural logarithm of the absolute value of the Jacobian determinant of the intrinsic -> observed map at e_obs, in the trace-determinant (ellipticity) convention.

Computes the natural logarithm of the absolute value of the Jacobian determinant of the intrinsic -> observed map at chi_obs, in the trace (distortion) convention.

Macro to generate the id function name for a background variable.

Declare the id function associated with obj_ns.

The implementation of the id function associated with obj_ns.

A convenience macro to define a subclass of NcXcorKernelComponent with a custom user data type.

A convenience macro to define a subclass of NcXcorLensingEfficiency with a custom user data type. This follows the same pattern as NcmIntegralND for inline type definition.

Default $\Omega_{r0}$.

Default $\Omega_{w0}$.

Default $w$.

Default $\Omega_{w0}$.

Default $w$.