ChiSquare Class
The ChiSquare Class within SORA was created to control the \(\chi^2\) minimization tests and obtain the best fit values and uncertainties. Here we have some useful tasks that allows the user to get the best value and uncertainty within a sigma uncertainty value, plot and save the values. The documentation here contains the details about every step.
This Jupyter-Notebook was designed as a tutorial for how to work with the ChiSquare Object Class. Any further question, please contact the core team: Altair Ramos Gomes Júnior, Bruno Eduardo Morgado, Gustavo Benedetti Rossi, and Rodrigo Carlos Boufleur.
The ChiSquare Docstring was designed to help the users. Also, each function has its Docstring containing its main purpose and the needed parameters (physical description and formats). Please, do not hesitate to use it.
0. Index
[1]:
## SORA package
from sora.extra import ChiSquare
## Usual packages
import numpy as np
import matplotlib.pyplot as pl
SORA version: 0.3
1. Instantiating a ChiSquare Object
The ChiSquare Class was not created to be instantiated by the user. Its main function is to control the fitting process and it will be resulting of the fitting tasks, such as LightCurve.occ_lcfit() and Occultation.fit_ellipse(). This Object contains a python dictionary with the \(\chi^2\) values and the associated tested parameters.
[2]:
ChiSquare?
Init signature: ChiSquare(chi2, npts, **kwargs)
Docstring:
Stores the arrays for all inputs and given chi-square.
Parameters
----------
chi2 : `array`
Array with all the chi-square values.
npts : `int`
Number of points used in the fit.
**kwargs
Any other given input must be an array with the same size as chi2. The
keyword `name` will be associated as the variable `name` of the given data.
Example
-------
>>> chisquare = ChiSquare(chi2, immersion=t1, emersion=t2)
``t1`` and ``t2`` must be an array with the same size as chi2.
The data can be accessed as
>>> chisquare.data['immersion']
File: ~/Documentos/códigos/SORA/sora/extra/chisquare.py
Type: type
Subclasses:
[3]:
chi2, t_immersion, t_emersion = np.loadtxt('input/ascii/example_chi2.dat',unpack=True)
chisquare = ChiSquare(chi2=chi2, npts=496, t_immersion=t_immersion, t_emersion=t_emersion)
2. Viewing the results
First, the value that minimizes the \(\chi^2\) can be obtained using the ChiSquare.get_values().
[4]:
chisquare.get_values()
[4]:
{'t_immersion': 76880.33436, 't_emersion': 76890.34416}
All the values within a sigma limit can be found in a similar manner
[5]:
chisquare.get_values(sigma=3)
[5]:
{'t_immersion': array([76880.37133, 76880.28921, 76880.24912, ..., 76880.29041,
76880.39328, 76880.43463]),
't_emersion': array([76890.26501, 76890.25714, 76890.37106, ..., 76890.42023,
76890.4073 , 76890.36891])}
The best-fitted value and its uncertainties can be obtained using ChiSquare.get_nsigma()
[6]:
chisquare.get_nsigma()
[6]:
{'chi2_min': 489.84066,
'sigma': 1,
'n_points': 137,
't_immersion': [76880.32901, 0.028059999996912666],
't_emersion': [76890.34104, 0.03118999999423977]}
[7]:
chisquare.get_nsigma(sigma=3)
[7]:
{'chi2_min': 489.84066,
'sigma': 3,
'n_points': 1719,
't_immersion': [76880.36540000001, 0.13475000000471482],
't_emersion': [76890.34015999999, 0.10841999999684049]}
Also, the number of fitted points (N) and the number of fitted parameters (P) can be obtained using ChiSquare.npts and ChiSquare.nparam
[8]:
print('Number of fitted points: {}'.format(chisquare.npts))
print('Number of fitted parameters: {}'.format(chisquare.nparam))
Number of fitted points: 496
Number of fitted parameters: 2
3. Saving the results and plots
The plot with the \(\chi^2\) by fitted parameter can be seen using ChiSquare.plot_chi2()
[9]:
chisquare.plot_chi2()
If the user choose to plot only one, it is possible to have complete control over it using matplotlib functions
[10]:
chisquare.plot_chi2('t_immersion')
pl.title('Occ. by Chariklo',fontsize=25)
pl.show()
The values within the ChiSquare object can be saved as an ASCII file using ChiSquare.to_file()
[11]:
chisquare.to_file('output/example_chi2.dat')
Two ChiSquare objects can be easily combined by adding them
[12]:
chisquare_2 = chisquare + chisquare
print('Single ChiSquare: ',len(chisquare.data['chi2']))
print('Combined ChiSquare:',len(chisquare_2.data['chi2']))
Single ChiSquare: 10000
Combined ChiSquare: 20000
This Jupyter-Notebook was designed as a tutorial for how to work with the ChiSquare Class. More information about the other classes, please refer to their specif Jupyter-Notebook. Any further question, please contact the core team: Altair Ramos Gomes Júnior, Bruno Eduardo Morgado, Gustavo Benedetti Rossi, and Rodrigo Carlos Boufleur.
The End