ArcCosine1D

class astropy.modeling.functional_models.ArcCosine1D(*args, meta=None, name=None, **kwargs)

Bases: _InverseTrigonometric1D

One dimensional ArcCosine returning values between 0 and pi only.

Parameters:

amplitudepython:float

Oscillation amplitude for corresponding Cosine

frequencypython:float

Oscillation frequency for corresponding Cosine

phasepython:float

Oscillation phase for corresponding Cosine

Other Parameters:

fixeda python: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

Cosine1D, ArcSine1D, ArcTangent1D

Notes

Model formula:

\[f(x) = ((arccos(x / A) / 2pi) - p) / f\]

The arccos function being used for this model will only accept inputs in [-A, A]; otherwise, a runtime warning will be thrown and the result will be NaN. To avoid this, the bounding_box has been properly set to accommodate this; therefore, it is recommended that this model always be evaluated with the with_bounding_box=True option.

Examples

import numpy as np
import matplotlib.pyplot as plt

from astropy.modeling.models import ArcCosine1D

plt.figure()
s1 = ArcCosine1D(amplitude=1, frequency=.25)
r=np.arange(-1, 1, .01)

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

plt.axis([-1, 1, 0, np.pi])
plt.show()

(png, svg, pdf)

Methods Summary

evaluate(x, amplitude, frequency, phase)	One dimensional ArcCosine model function
fit_deriv(x, amplitude, frequency, phase)	One dimensional ArcCosine model derivative

Methods Documentation

static evaluate(x, amplitude, frequency, phase)

One dimensional ArcCosine model function

static fit_deriv(x, amplitude, frequency, phase)

One dimensional ArcCosine model derivative