Tangent1D

class astropy.modeling.functional_models.Tangent1D(*args, meta=None, name=None, **kwargs)

Bases: _Trigonometric1D

One dimensional Tangent model.

Parameters:

amplitudepython:float

Oscillation amplitude

frequencypython:float

Oscillation frequency

phasepython:float

Oscillation phase

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

Sine1D, Cosine1D, Const1D, Linear1D

Notes

Model formula:

\[f(x) = A \tan(2 \pi f x + 2 \pi p)\]

Note that the tangent function is undefined for inputs of the form pi/2 + n*pi for all integers n. Thus thus the default bounding box has been restricted to:

\[[(-1/4 - p)/f, (1/4 - p)/f]\]

which is the smallest interval for the tangent function to be continuous on.

Examples

import numpy as np
import matplotlib.pyplot as plt

from astropy.modeling.models import Tangent1D

plt.figure()
s1 = Tangent1D(amplitude=1, frequency=.25)
r=np.arange(0, 10, .01)

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

plt.axis([0, 10, -5, 5])
plt.show()

(png, svg, pdf)

Methods Summary

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

Methods Documentation

static evaluate(x, amplitude, frequency, phase)

One dimensional Tangent model function

static fit_deriv(x, amplitude, frequency, phase)

One dimensional Tangent model derivative