PowerLaw1D¶
-
class
astropy.modeling.powerlaws.
PowerLaw1D
(amplitude=1, x_0=1, alpha=1, **kwargs)[source] [edit on github]¶ Bases:
astropy.modeling.Fittable1DModel
One dimensional power law model.
Parameters: - amplitude : float
Model amplitude at the reference point
- x_0 : float
Reference point
- alpha : float
Power law index
Other Parameters: - fixed : a dict, optional
A dictionary
{parameter_name: boolean}
of parameters to not be varied during fitting. True means the parameter is held fixed. Alternatively thefixed
property of a parameter may be used.- tied : dict, optional
A dictionary
{parameter_name: callable}
of parameters which are linked to some other parameter. The dictionary values are callables providing the linking relationship. Alternatively thetied
property of a parameter may be used.- bounds : dict, optional
A dictionary
{parameter_name: value}
of lower and upper bounds of parameters. Keys are parameter names. Values are a list or a tuple of length 2 giving the desired range for the parameter. Alternatively, themin
andmax
properties of a parameter may be used.- eqcons : list, optional
A list of functions of length
n
such thateqcons[j](x0,*args) == 0.0
in a successfully optimized problem.- ineqcons : list, optional
A list of functions of length
n
such thatieqcons[j](x0,*args) >= 0.0
is a successfully optimized problem.
Notes
Model formula (with \(A\) for
amplitude
and \(\alpha\) foralpha
):\[f(x) = A (x / x_0) ^ {-\alpha}\]Attributes Summary
alpha
amplitude
input_units
This property is used to indicate what units or sets of units the evaluate method expects, and returns a dictionary mapping inputs to units (or None
if any units are accepted).param_names
x_0
Methods Summary
evaluate
(x, amplitude, x_0, alpha)One dimensional power law model function fit_deriv
(x, amplitude, x_0, alpha)One dimensional power law derivative with respect to parameters Attributes Documentation
-
alpha
¶
-
amplitude
¶
-
input_units
¶ This property is used to indicate what units or sets of units the evaluate method expects, and returns a dictionary mapping inputs to units (or
None
if any units are accepted).Model sub-classes can also use function annotations in evaluate to indicate valid input units, in which case this property should not be overridden since it will return the input units based on the annotations.
-
param_names
= ('amplitude', 'x_0', 'alpha')¶
-
x_0
¶
Methods Documentation
-
static
evaluate
(x, amplitude, x_0, alpha)[source] [edit on github]¶ One dimensional power law model function
-
static
fit_deriv
(x, amplitude, x_0, alpha)[source] [edit on github]¶ One dimensional power law derivative with respect to parameters