Box1D

class astropy.modeling.functional_models.Box1D(amplitude=1, x_0=0, width=1, **kwargs)

Bases: Fittable1DModel

One dimensional Box model.

Parameters:

amplitudepython:float

Amplitude A

x_0python:float

Position of the center of the box function

widthpython:float

Width of the box

Other Parameters:

fixedpython: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.

tiedpython: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 the tied property of a parameter may be used.

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

eqconspython:list, optional

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

ineqconspython:list, optional

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

See also

Box2D, TrapezoidDisk2D

Notes

Model formula:

\[\begin{split}f(x) = \left \{ \begin{array}{ll} A & : x_0 - w/2 \leq x \leq x_0 + w/2 \\ 0 & : \text{else} \end{array} \right.\end{split}\]

Examples

import numpy as np
import matplotlib.pyplot as plt

from astropy.modeling.models import Box1D

plt.figure()
s1 = Box1D()
r = np.arange(-5, 5, .01)

for factor in range(1, 4):
    s1.amplitude = factor
    s1.width = factor
    plt.plot(r, s1(r), color=str(0.25 * factor), lw=2)

plt.axis([-5, 5, -1, 4])
plt.show()

(png, svg, pdf)

Attributes Summary

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.
return_units	This property is used to indicate what units or sets of units the output of evaluate should be in, and returns a dictionary mapping outputs to units (or None if any units are accepted).
width
x_0

Methods Summary

evaluate(x, amplitude, x_0, width)

One dimensional Box model function.

Attributes Documentation

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

input_units

param_names = ('amplitude', 'x_0', 'width')

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.

return_units

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

x_0 = Parameter('x_0', value=0.0)

Methods Documentation

static evaluate(x, amplitude, x_0, width)

One dimensional Box model function.