# PowerLaw1D¶

class astropy.modeling.powerlaws.PowerLaw1D(amplitude=1, x_0=1, alpha=1, **kwargs)[source]

One dimensional power law model.

Parameters
amplitudefloat

Model amplitude at the reference point

x_0float

Reference point

alphafloat

Power law index

Other Parameters
fixeda dict, optional

A dictionary {parameter_name: boolean} of parameters to not be varied during fitting. True means the parameter is held fixed. Alternatively the fixed property of a parameter may be used.

tieddict, 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 the tied property of a parameter may be used.

boundsdict, 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, the min and max properties of a parameter may be used.

eqconslist, optional

A list of functions of length n such that eqcons[j](x0,*args) == 0.0 in a successfully optimized problem.

ineqconslist, optional

A list of functions of length n such that ieqcons[j](x0,*args) >= 0.0 is a successfully optimized problem.

Notes

Model formula (with $$A$$ for amplitude and $$\alpha$$ for alpha):

$f(x) = A (x / x_0) ^ {-\alpha}$

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 Names of the parameters that describe models of this type. 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 = Parameter('alpha', value=1.0)
amplitude = Parameter('amplitude', value=1.0)
input_units
param_names = ('amplitude', 'x_0', 'alpha')

Names of the parameters that describe models of this type.

The parameters in this tuple are in the same order they should be passed in when initializing a model of a specific type. Some types of models, such as polynomial models, have a different number of parameters depending on some other property of the model, such as the degree.

When defining a custom model class the value of this attribute is automatically set by the Parameter attributes defined in the class body.

x_0 = Parameter('x_0', value=1.0)

Methods Documentation

static evaluate(x, amplitude, x_0, alpha)[source]

One dimensional power law model function

static fit_deriv(x, amplitude, x_0, alpha)[source]

One dimensional power law derivative with respect to parameters