pyboundfit

Boundary fits using polynomials or splines, based on the method described in Cardiel 2009. This code is a Python implementation of part of the functionality implemented in the original Fortran 77 code boundfit.

The numerical minimization of the fit to splines is performed with the help of the package lmfit.

Warning: this code is under development. Major changes are still being introduced.

Instaling the code

In order to keep your Python installation clean, it is highly recommended to first build a specific Python 3 virtual enviroment

Creating and activating the Python virtual environment

$ python3 -m venv venv_pyboundfit
$ . venv_pyboundfit/bin/activate
(venv_pyboundfit) $ 

Installing the package

The latest stable version is available via de PyPI repository:

(venv_pyboundfit) $ pip install pyboundfit

Note: This command can also be employed in a Windows terminal opened through the CMD.exe prompt icon available in Anaconda Navigator.

The latest development version is available through GitHub:

(venv_pyboundfit) $ pip install git+https://github.com/nicocardiel/pyboundfit.git@main#egg=pyboundfit

Testing the installation

(venv_pyboundfit) $ pip show pyboundfit

(venv_pyboundfit) $ ipython

In [1]: import pyboundfit

In [2]: print(pyboundfit.__version__)
0.3.0

In [3]: pol1, pol2, spl1, spl2 = pyboundfit.demo()
Computing upper boundary (polynomial fit)... OK!
Computing lower boundary (polynomial fit)... OK!
Computing upper boundary (splines fit)... OK!
Computing lower boundary (splines fit)... OK!

In [4]: pol1.coef
Out[4]: 
array([  22.43919975,  -41.5216713 ,   -7.32451917,  140.23297889,
         41.59855497, -148.66578342])
...

The demo function computes the boundary fits to some example data and generates the following plot:

Usage

Import the required packages

import matplotlib.pyplot as plt
import numpy as np
import pyboundfit as bf

Generate some random data to be fitted

npoints = 300
rng = np.random.default_rng(seed=1234)
xfit = np.linspace(1.0, 3.5, npoints)
yfit = np.sin(xfit) + rng.normal(loc=0, scale=0.1, size=npoints)

Fit upper and lower boundaries using polynomials

pol_upper = bf.boundfit_poly(
    x=xfit, y=yfit, deg=5, 
    xi=10, niter=100, expweight=True,
    boundary='upper'
)
pol_lower = bf.boundfit_poly(
    x=xfit, y=yfit, deg=5, 
    xi=10, niter=100, expweight=True,
    boundary='lower'
)

Fit upper and lower boundaries using splines (the numerical minimization takes some time).

spl_upper = bf.boundfit_adaptive_splines(
    x=xfit, y=yfit, t=5, 
    xi=100, niter=100, boundary='upper',
    adaptive=False,
    expweight=True
)
spl_lower = bf.boundfit_adaptive_splines(
    x=xfit, y=yfit, t=5, 
    xi=100, niter=100, boundary='lower',
    adaptive=False,
    expweight=True
)

Display the result

import matplotlib.pyplot as plt
fig, ax = plt.subplots()
ax.plot(xfit, yfit, 'ko')
ax.plot(xfit, pol_upper(xfit), '-', label='upper boundary (polynomial)')
ax.plot(xfit, pol_lower(xfit), '-', label='lower boundary (polynomial)')
ax.plot(xfit, spl_upper(xfit), ':', label='upper boundary (splines)')
ax.plot(xfit, spl_lower(xfit), ':', label='lower boundary (splines)')
ax.set_xlabel('X axis')
ax.set_ylabel('Y axis')
ax.legend()
plt.tight_layout()
plt.show()

Please, note that the results are quite sensitive to the fitting parameters.

Citation

If you find this package useful, please cite Cardiel 2009.

@ARTICLE{2009MNRAS.396..680C,
       author = {{Cardiel}, N.},
        title = "{Data boundary fitting using a generalized least-squares method}",
      journal = {\mnras},
     keywords = {methods: data analysis, methods: numerical, Astrophysics - Instrumentation and Methods for Astrophysics},
         year = 2009,
        month = jun,
       volume = {396},
       number = {2},
        pages = {680-695},
          doi = {10.1111/j.1365-2966.2009.14749.x},
archivePrefix = {arXiv},
       eprint = {0903.2068},
 primaryClass = {astro-ph.IM},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2009MNRAS.396..680C},
      adsnote = {Provided by the SAO/NASA Astrophysics Data Syste