classylss.binding.
Background
(ClassEngine engine)¶Bases: object
A wrapper of the background module in CLASS.
Parameters: | engine (ClassEngine) – the CLASS engine object |
---|
Attributes
C |
The speed of light in units of km/s. |
G |
The gravitational constant in units of \(10^{-10} \ (M_\odot/h)^{-1} (\mathrm{Mpc}/h) \mathrm{km}^2 \mathrm{s}^{-2}\). |
H0 |
Current Hubble parameter in units of \(\mathrm{km/s} (\mathrm{Mpc}/h)^{-1}.\) |
N_ncdm |
The number of distinguishable ncdm (massive neutrino) species. |
N_ur |
The number of ultra-relativistic species. |
Neff |
Effective number of relativistic species, summed over ultra-relativistic and ncdm species. |
Omega0_b |
Current density parameter for photons, \(\Omega_{b,0}\). |
Omega0_cdm |
Current density parameter for cold dark matter, \(\Omega_{cdm,0}\). |
Omega0_dcdm |
Current density parammeter for decaying cold dark matter, \(\Omega_{dcdm,0}\). |
Omega0_fld |
Current density parameter for dark energy (fluid) \(\Omega_{fld, 0}\). |
Omega0_g |
Current density parameter for photons, \(\Omega_{g,0}\). |
Omega0_k |
Current density parameter for curvaturve, \(\Omega_{k,0}\). |
Omega0_lambda |
Current density parameter for cosmological constant, \(\Omega_{\Lambda,0}\). |
Omega0_m |
The sum of density parameters for all non-relativistic components, \(\Omega_{0,m}\). |
Omega0_ncdm |
Current density parameter for distinguishable (massive) neutrinos for each species as an array, \(\Omega_{0, ncdm}\). |
Omega0_ncdm_tot |
Current total density parameter of all distinguishable (massive) neutrinos. |
Omega0_pncdm |
The pressure contribution to the current density parameter for the non-relativatistic part of massive neutrinos (an array holding all species). |
Omega0_pncdm_tot |
The sum of \(\Omega_{0,pncdm}\) for all species. |
Omega0_r |
Current density parameter of radiation, \(\Omega_{0,r}\). |
Omega0_ur |
Current density parameter of ultra-relativistic (massless) neutrinos, \(\Omega_{0,\nu_r}\). |
T0_cmb |
The current CMB temperature in Kelvins. |
T0_ncdm |
An array holding the current ncdm temperature in Kelvins for each species. |
a_max |
The maximum scale factor for which results can be computed; it can be greater than 1.0. |
a_today |
An arbitrary number that sets the reference scaling factor. |
age0 |
The current age of the universe in gigayears. |
data |
|
h |
The dimensionless Hubble parameter. |
m_ncdm |
The masses of the distinguishable ncdm (massive neutrino) species, in units of eV. |
w0_fld |
Current fluid equation of state parameter, \(w_{0,fld}\). |
wa_fld |
Fluid equation of state derivative, \(w_{a,fld}\). |
Methods
Omega_b (self, z) |
Density parameter of baryons. |
Omega_cdm (self, z) |
Density parameter of cold dark matter. |
Omega_fld (self, z) |
Density parameter of dark energy (fluid). |
Omega_g (self, z) |
Density parameter of photons. |
Omega_k (self, z) |
Density parameter of curvature. |
Omega_lambda (self, z) |
Density of dark energy (cosmological constant). |
Omega_m (self, z) |
Density parameter of non-relativistic (matter-like) component, including non-relativistic part of massive neutrino. |
Omega_ncdm (self, z[, species]) |
Density parameter of massive neutrinos. |
Omega_pncdm (self, z[, species]) |
Return \(\Omega_{pncdm}\) as a function redshift. |
Omega_r (self, z) |
Density parameter of relativistic (radiation-like) component, including relativistic part of massive neutrino and massless neutrino. |
Omega_ur (self, z) |
Density parameter of ultra relativistic neutrinos. |
T_cmb (self, z) |
The CMB temperature as a function of redshift. |
T_ncdm (self, z) |
The ncdm temperature (massive neutrinos) as a function of redshift. |
angular_diameter_distance (self, z) |
Angular diameter distance in \(\mathrm{Mpc}/h\) at a given redshift. |
comoving_distance (self, z) |
Comoving line-of-sight distance in \(\mathrm{Mpc}/h\) at a given redshift. |
comoving_transverse_distance (self, z) |
Comoving transverse distance in \(\mathrm{Mpc}/h\) at a given redshift. |
compute_for_z (self, z, int column) |
Internal function to compute the background module at a specific redshift. |
efunc (self, z) |
Function giving \(E(z)\), where the Hubble parameter is defined as \(H(z) = H_0 E(z)\). |
efunc_prime (self, z) |
Function giving \(dE(z) / da\). |
hubble_function (self, z) |
The Hubble function in CLASS units, returning ba.index_bg_H . |
hubble_function_prime (self, z) |
Derivative of Hubble function: \(dH/d\tau\), where \(d\tau/da = 1 / (a^2 H)\) in CLASS units. |
luminosity_distance (self, z) |
Luminosity distance in \(\mathrm{Mpc}/h\) at redshift z . |
p_ncdm (self, z[, species]) |
Pressure of non-relative part of massive neutrino. |
rho_b (self, z) |
Density of baryons \(\rho_b\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\). |
rho_cdm (self, z) |
Density of cold dark matter \(\rho_{cdm}\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\). |
rho_crit (self, z) |
Critical density excluding curvature \(\rho_c\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\). |
rho_fld (self, z) |
Density of dark energy fluid \(\rho_{fld}\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\). |
rho_g (self, z) |
Density of photons \(\rho_g\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\). |
rho_k (self, z) |
Density of curvature \(\rho_k\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\). |
rho_lambda (self, z) |
Density of cosmological constant \(\rho_\Lambda\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\). |
rho_m (self, z) |
Density of matter \(\rho_b\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\). |
rho_ncdm (self, z[, species]) |
Density of non-relativistic part of massive neutrinos \(\rho_{ncdm}\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\). |
rho_r (self, z) |
Density of radiation \(\rho_r\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\). |
rho_tot (self, z) |
Total density \(\rho_\mathrm{tot}\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\). |
rho_ur (self, z) |
Density of ultra-relativistic radiation (massless neutrinos) \(\rho_{ur}\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\). |
scale_independent_growth_factor (self, z) |
Return the scale invariant growth factor \(D(a)\) for CDM perturbations. |
scale_independent_growth_rate (self, z) |
The scale invariant growth rate \(d\mathrm{ln}D/d\mathrm{ln}a\) for CDM perturbations. |
tau (self, z) |
Conformal time, equal to comoving distance when K = 0.0 (flat universe). |
time (self, z) |
Proper time (age of universe) in gigayears. |
C
¶The speed of light in units of km/s.
G
¶The gravitational constant in units of \(10^{-10} \ (M_\odot/h)^{-1} (\mathrm{Mpc}/h) \mathrm{km}^2 \mathrm{s}^{-2}\).
H0
¶Current Hubble parameter in units of \(\mathrm{km/s} (\mathrm{Mpc}/h)^{-1}.\)
N_ncdm
¶The number of distinguishable ncdm (massive neutrino) species.
N_ur
¶The number of ultra-relativistic species.
This is equal to:
Neff
¶Effective number of relativistic species, summed over ultra-relativistic and ncdm species.
Omega0_b
¶Current density parameter for photons, \(\Omega_{b,0}\).
Omega0_cdm
¶Current density parameter for cold dark matter, \(\Omega_{cdm,0}\).
Omega0_dcdm
¶Current density parammeter for decaying cold dark matter, \(\Omega_{dcdm,0}\).
Omega0_fld
¶Current density parameter for dark energy (fluid) \(\Omega_{fld, 0}\).
Omega0_g
¶Current density parameter for photons, \(\Omega_{g,0}\).
Omega0_k
¶Current density parameter for curvaturve, \(\Omega_{k,0}\).
Omega0_lambda
¶Current density parameter for cosmological constant, \(\Omega_{\Lambda,0}\).
Omega0_m
¶The sum of density parameters for all non-relativistic components,
\(\Omega_{0,m}\). The value differs from Om0
in astropy
.
This is equal to:
Omega0_ncdm
¶Current density parameter for distinguishable (massive) neutrinos for each species as an array, \(\Omega_{0, ncdm}\).
Omega0_ncdm_tot
¶Current total density parameter of all distinguishable (massive) neutrinos.
Omega0_pncdm
¶The pressure contribution to the current density parameter for the non-relativatistic part of massive neutrinos (an array holding all species).
Omega0_pncdm_tot
¶The sum of \(\Omega_{0,pncdm}\) for all species.
Omega0_r
¶Current density parameter of radiation, \(\Omega_{0,r}\). This is equal to:
Omega0_ur
¶Current density parameter of ultra-relativistic (massless) neutrinos, \(\Omega_{0,\nu_r}\).
Omega_b
(self, z)¶Density parameter of baryons.
Omega_cdm
(self, z)¶Density parameter of cold dark matter.
Omega_fld
(self, z)¶Density parameter of dark energy (fluid).
Omega_g
(self, z)¶Density parameter of photons.
Omega_k
(self, z)¶Density parameter of curvature.
Omega_lambda
(self, z)¶Density of dark energy (cosmological constant).
Omega_m
(self, z)¶Density parameter of non-relativistic (matter-like) component, including non-relativistic part of massive neutrino. Unit
Omega_ncdm
(self, z, species=None)¶Density parameter of massive neutrinos.
Omega_pncdm
(self, z, species=None)¶Return \(\Omega_{pncdm}\) as a function redshift.
Omega_r
(self, z)¶Density parameter of relativistic (radiation-like) component, including relativistic part of massive neutrino and massless neutrino.
Omega_ur
(self, z)¶Density parameter of ultra relativistic neutrinos.
T0_cmb
¶The current CMB temperature in Kelvins.
T0_ncdm
¶An array holding the current ncdm temperature in Kelvins for each species.
T_cmb
(self, z)¶The CMB temperature as a function of redshift.
T_ncdm
(self, z)¶The ncdm temperature (massive neutrinos) as a function of redshift.
Return shape is (N_ncdm,) if N_ncdm == 1 else (len(z), N_ncdm)
a_max
¶The maximum scale factor for which results can be computed; it can be greater than 1.0.
a_today
¶An arbitrary number that sets the reference scaling factor. It shall be 1 usually.
age0
¶The current age of the universe in gigayears.
angular_diameter_distance
(self, z)¶Angular diameter distance in \(\mathrm{Mpc}/h\) at a given redshift.
This gives the proper (sometimes called ‘physical’) transverse
distance corresponding to an angle of 1 radian for an object
at redshift z
.
It is equal to the comoving transverse distance divided by \(1+z\).
See eq. 18 of astro-ph/9905116 for \(D_A(z)\).
comoving_distance
(self, z)¶Comoving line-of-sight distance in \(\mathrm{Mpc}/h\) at a given redshift.
The comoving distance along the line-of-sight between two objects remains constant with time for objects in the Hubble flow.
See eq. 15 of astro-ph/9905116 for \(D_C(z)\).
comoving_transverse_distance
(self, z)¶Comoving transverse distance in \(\mathrm{Mpc}/h\) at a given redshift.
This value is the transverse comoving distance at redshift z
corresponding to an angular separation of 1 radian. This is
the same as the comoving distance in a flat universe.
See eq. 16 of astro-ph/9905116 for \(D_M(z)\).
compute_for_z
(self, z, int column)¶Internal function to compute the background module at a specific redshift.
data
¶efunc
(self, z)¶Function giving \(E(z)\), where the Hubble parameter is defined as \(H(z) = H_0 E(z)\).
efunc_prime
(self, z)¶Function giving \(dE(z) / da\).
h
¶The dimensionless Hubble parameter.
hubble_function
(self, z)¶The Hubble function in CLASS units, returning ba.index_bg_H
.
Users should use efunc()
instead.
hubble_function_prime
(self, z)¶Derivative of Hubble function: \(dH/d\tau\), where \(d\tau/da = 1 / (a^2 H)\) in CLASS units.
Users should use efunc_prime()
instead.
luminosity_distance
(self, z)¶Luminosity distance in \(\mathrm{Mpc}/h\) at redshift z
.
This is the distance to use when converting between the
bolometric flux from an object at redshift z
and its
bolometric luminosity.
It is equal to the comoving transverse distance times \(1+z\).
See eq. 21 of astro-ph/9905116 for \(D_L(z)\).
m_ncdm
¶The masses of the distinguishable ncdm (massive neutrino) species, in units of eV.
p_ncdm
(self, z, species=None)¶Pressure of non-relative part of massive neutrino.
rho_b
(self, z)¶Density of baryons \(\rho_b\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\).
rho_cdm
(self, z)¶Density of cold dark matter \(\rho_{cdm}\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\).
rho_crit
(self, z)¶Critical density excluding curvature \(\rho_c\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\).
This is defined as:
rho_fld
(self, z)¶Density of dark energy fluid \(\rho_{fld}\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\).
rho_g
(self, z)¶Density of photons \(\rho_g\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\).
rho_k
(self, z)¶Density of curvature \(\rho_k\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\).
Note: this is defined such that
rho_lambda
(self, z)¶Density of cosmological constant \(\rho_\Lambda\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\).
rho_m
(self, z)¶Density of matter \(\rho_b\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\).
rho_ncdm
(self, z, species=None)¶Density of non-relativistic part of massive neutrinos \(\rho_{ncdm}\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\).
rho_r
(self, z)¶Density of radiation \(\rho_r\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\).
rho_tot
(self, z)¶Total density \(\rho_\mathrm{tot}\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\). It is usually close to 27.76.
rho_ur
(self, z)¶Density of ultra-relativistic radiation (massless neutrinos) \(\rho_{ur}\) as a function of redshift, in units of \(10^{10} (M_\odot/h) (\mathrm{Mpc}/h)^{-3}\).
scale_independent_growth_factor
(self, z)¶Return the scale invariant growth factor \(D(a)\) for CDM perturbations.
This is the quantity defined by CLASS as index_bg_D
in the
background module.
scale_independent_growth_rate
(self, z)¶The scale invariant growth rate \(d\mathrm{ln}D/d\mathrm{ln}a\) for CDM perturbations.
This is the quantity defined by CLASS as index_bg_f
in the
background module.
tau
(self, z)¶Conformal time, equal to comoving distance when K = 0.0 (flat universe). In units of \(\mathrm{Mpc}\) as in CLASS.
time
(self, z)¶Proper time (age of universe) in gigayears.
w0_fld
¶Current fluid equation of state parameter, \(w_{0,fld}\).
wa_fld
¶Fluid equation of state derivative, \(w_{a,fld}\).
classylss.binding.
ClassBadValueError
¶Bases: ValueError
Raised when Class could not compute the cosmology at this point.
This will be caught by the parameter extraction code to give an extremely unlikely value to this point
args
¶with_traceback
()¶Exception.with_traceback(tb) – set self.__traceback__ to tb and return self.
classylss.binding.
ClassEngine
(pars={})¶Bases: object
The default CLASS engine class, which initializes CLASS from an input set of parameters.
Parameters: | pars (dict, optional) – a dictionary of parameters to initialize CLASS with |
---|
Attributes
parameter_file |
A string holding the parameter names and values as loaded by CLASS. |
parameter_file
¶A string holding the parameter names and values as loaded by CLASS.
classylss.binding.
ClassParserError
¶Bases: ValueError
args
¶with_traceback
()¶Exception.with_traceback(tb) – set self.__traceback__ to tb and return self.
classylss.binding.
ClassRuntimeError
¶Bases: RuntimeError
args
¶with_traceback
()¶Exception.with_traceback(tb) – set self.__traceback__ to tb and return self.
classylss.binding.
Perturbs
(ClassEngine engine)¶Bases: object
A wrapper of the perturbs module in CLASS.
Parameters: | engine (ClassEngine) – the CLASS engine object |
---|
Attributes
P_z_max |
The input parameter specifying the maximum redshift measured for power spectra. |
gauge |
The gauge name as a string, either ‘newtonian’ or ‘synchronous’. |
k_max_for_pk |
The input parameter specifying the maximum k value to compute spectra for; units of \(h \mathrm{Mpc}^{-1}\). |
P_z_max
¶The input parameter specifying the maximum redshift measured for power spectra.
gauge
¶The gauge name as a string, either ‘newtonian’ or ‘synchronous’.
k_max_for_pk
¶The input parameter specifying the maximum k
value to compute
spectra for; units of \(h \mathrm{Mpc}^{-1}\).
classylss.binding.
Primordial
(ClassEngine engine)¶Bases: object
A wrapper of the primordial module in CLASS.
Parameters: | engine (ClassEngine) – the CLASS engine object |
---|
Methods
get_pk (self, k) |
The primoridal spectrum at k . |
get_primordial (self) |
Return the primordial scalar and/or tensor spectrum depending on ‘modes’. |
get_pk
(self, k)¶The primoridal spectrum at k
. This is defined as:
See also: equation 2 of this reference.
Parameters: | k (array_like) – wavenumbers in \(h \mathrm{Mpc}^{-1}\) units. |
---|---|
Returns: | the primordial power |
Return type: | array_like |
get_primordial
(self)¶Return the primordial scalar and/or tensor spectrum depending on ‘modes’.
The ‘output’ parameter must be set to something, e.g. ‘tCl’.
Returns: | structured array containing k-vector and primordial scalar and tensor \(P(k)\). |
---|---|
Return type: | array_like |
classylss.binding.
Spectra
(ClassEngine engine)¶Bases: object
A wrapper of the spectra module in CLASS.
Parameters: | engine (ClassEngine) – the CLASS engine object |
---|
Attributes
A_s |
The scalar amplitude of the primordial power spectrum at \(k_\mathrm{pivot}\). |
P_k_max |
The maximum k value measured for power spectra in \(h \mathrm{Mpc}^{-1}\). |
P_k_min |
The minimum k value for which power spectra have been computed in \(h \mathrm{Mpc}^{-1}\). |
data |
|
has_pk_matter |
Boolean flag specifying whether matter power spectra have been requested as output. |
k_pivot |
The primordial power spectrum pivot scale, where the primordial power is equal to \(A_s\). |
ln_1e10_A_s |
Return \(\log(10^{10}A_s)\). |
n_s |
The tilt of the primordial power spectrum. |
nonlinear |
Boolean flag specifying whether the power spectrum is nonlinear. |
sigma8 |
The amplitude of matter fluctuations at \(z=0\). |
Methods
get_pk (self, k, z) |
The primary power spectrum result (nonlinear if enabled) on k and z array. |
get_pklin (self, k, z) |
Linear power spectrum result (linear even if nonlinear is enabled) on k and z array. |
get_transfer (self, z[, output_format]) |
Return the density and/or velocity transfer functions for all initial conditions today. |
sigma8_z (self, z) |
Return \(\sigma_8(z)\). |
A_s
¶The scalar amplitude of the primordial power spectrum at \(k_\mathrm{pivot}\).
P_k_max
¶The maximum k
value measured for power spectra in
\(h \mathrm{Mpc}^{-1}\).
P_k_min
¶The minimum k
value for which power spectra have been computed in
\(h \mathrm{Mpc}^{-1}\).
This is computed from the ln_k
array of the Spectra module.
data
¶get_pk
(self, k, z)¶The primary power spectrum result (nonlinear if enabled) on k
and
z
array.
Parameters: | |
---|---|
Returns: | the power spectrum in units of \((\mathrm{Mpc}/h)^3\) |
Return type: | array like |
get_pklin
(self, k, z)¶Linear power spectrum result (linear even if nonlinear is enabled)
on k
and z
array.
Parameters: | |
---|---|
Returns: | the power spectrum in units of \((\mathrm{Mpc}/h)^3\) |
Return type: | array like |
get_transfer
(self, z, output_format='class')¶Return the density and/or velocity transfer functions for all initial
conditions today. You must include ‘dCl’ and ‘vCl’ in the list of
‘output’. The transfer functions can also be computed at higher
redshift z
provided that ‘z_pk’ has been set and that z
is
inside the region spanned by ‘z_pk’.
This function is not vectorized because it returns a vector when ‘ic_size’ is greater than 1, and we don’t understand ‘ic_size’.
Parameters: |
|
---|---|
Returns: | tk – array containing transfer functions. |
Return type: | array_like |
has_pk_matter
¶Boolean flag specifying whether matter power spectra have been requested as output.
k_pivot
¶The primordial power spectrum pivot scale, where the primordial power is equal to \(A_s\). Units of \(h \mathrm{Mpc}^{-1}\).
ln_1e10_A_s
¶Return \(\log(10^{10}A_s)\).
n_s
¶The tilt of the primordial power spectrum.
nonlinear
¶Boolean flag specifying whether the power spectrum is nonlinear.
sigma8
¶The amplitude of matter fluctuations at \(z=0\).
sigma8_z
(self, z)¶Return \(\sigma_8(z)\).
classylss.binding.
Thermo
(ClassEngine engine)¶Bases: object
A wrapper of the thermo module in CLASS.
Parameters: | engine (ClassEngine) – the CLASS engine object |
---|
Attributes
rs_drag |
The comoving sound horizon at baryon drag, in \(\mathrm{Mpc}/h\). |
rs_rec |
The comoving sound horizon at recombination, \(z=z_\mathrm{rec}\). |
tau_reio |
The reionization optical depth. |
theta_s |
The sound horizon angle at recombination, equal to \(r_s(z_\mathrm{rec}) / D_a(z_\mathrm{rec})\). |
z_drag |
The baryon drag redshift. |
z_rec |
The redshift at which the visibility reaches its maximum; equals the recombination redshift. |
z_reio |
The reionization redshift. |
rs_drag
¶The comoving sound horizon at baryon drag, in \(\mathrm{Mpc}/h\).
rs_rec
¶The comoving sound horizon at recombination, \(z=z_\mathrm{rec}\). Units of \(\mathrm{Mpc}/h\).
tau_reio
¶The reionization optical depth.
theta_s
¶The sound horizon angle at recombination, equal to \(r_s(z_\mathrm{rec}) / D_a(z_\mathrm{rec})\).
z_drag
¶The baryon drag redshift.
z_rec
¶The redshift at which the visibility reaches its maximum; equals the recombination redshift.
z_reio
¶The reionization redshift.
classylss.binding.
val2str
(val)¶