PowerLaw1D#

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

Bases: Fittable1DModel

One dimensional power law model.

Parameters:

amplitudefloat: Model amplitude at the reference point
x_0float: Reference point
alphafloat: Power law index

Other Parameters:

fixeddict, 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.

See also

BrokenPowerLaw1D, ExponentialCutoffPowerLaw1D, LogParabola1D

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.