pynbody.analysis.theoretical_profiles.AbstractBaseProfile

class pynbody.analysis.theoretical_profiles.AbstractBaseProfile

Bases: ABC

Represents an analytic profile of a halo, and provides a method to fit the profile to data.

The class is organised a dictionary, i.e. profile parameters of a given instance can be accessed through profile['...'] and the available parameters are listed in profile.keys(). The parameters are set at initialisation and cannot be changed afterwards.

To define a new profile, create a new class inheriting from this base class and define your own profile_functional() method. The static version can be handy to avoid having to create and object every time. As a example, the NFW functional is implemented.

A generic fitting function is provided (fit()). Given a binned quantity as a function of radius, it uses least-squares to fit the given functional form to the data.

Methods

enclosed_mass(radius)	Return the mass, M(r), enclosed within a given radius
fit(radial_data, profile_data[, ...])	Fit the given profile using a least-squares method.
keys()	Return the keys of the profile parameters
logarithmic_slope(radius)	Return the logarithmic slope of the profile, d ln rho / d ln r, at a given radius
parameter_bounds(r_values, rho_values)	Return bounds on the parameter values for the profile fit

__init__()

abstract enclosed_mass(radius)

Return the mass, M(r), enclosed within a given radius

classmethod fit(radial_data, profile_data, profile_err=None, use_analytical_jac=True, guess=None, verbose=0, return_profile=True)

Fit the given profile using a least-squares method.

Parameters:

• radial_data (array_like) – The central radius of the bins in which the profile data is measured

• profile_data (array_like) – The profile density values

• profile_err (array_like, optional) – The error on the profile data

• use_analytical_jac (bool) – Whether to use the analytical jacobian of the profile function. If False, finite differencing is used.

• guess (array_like, optional) – An initial guess for the parameters of the profile. If None, the initial guess is taken to be all ones, according to the underlying scipy.optimize.curve_fit function.

• verbose (int) – The verbosity level to pass to the underlying scipy.optimize.curve_fit function.

• return_profile (bool) – Whether to return the profile object or just the parameters

Returns:

• fitted_profile (array_like | AbstractBaseProfile) – If return_profile is True, the fitted profile object. Otherwise, the fitted parameters.

• cov (array_like) – The covariance matrix of the fit. The diagonal elements are the variance of the parameters.

keys()

Return the keys of the profile parameters

abstract logarithmic_slope(radius)

Return the logarithmic slope of the profile, d ln rho / d ln r, at a given radius

abstract classmethod parameter_bounds(r_values, rho_values)

Return bounds on the parameter values for the profile fit

Parameters:

• r_values (array_like) – The radii at which the profile is measured

• rho_values (array_like) – The density values of the profile

Returns:

bounds – A 2-tuple containing lower and upper bounds respectively for the parameters of the profile

Return type:

tuple[array_like]