#!/usr/bin/env python
# -*- coding: utf-8 -*-
# The MIT License (MIT)
# Copyright (c) 2017 Juan Cabral
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
# The above copyright notice and this permission notice shall be included in
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# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.
# =============================================================================
# FUTURE
# =============================================================================
from __future__ import unicode_literals
# =============================================================================
# DOC
# =============================================================================
__doc__ = """"""
# =============================================================================
# IMPORTS
# =============================================================================
import numpy as np
from .core import Extractor
# =============================================================================
# EXTRACTOR CLASS
# =============================================================================
[docs]class Eta_e(Extractor):
r"""
**Eta_e** (:math:`\eta^e`)
Variability index :math:`\eta` is the ratio of the mean of the square of
successive differences to the variance of data points. The index was
originally proposed to check whether the successive data points are
independent or not. In other words, the index was developed to check if
any trends exist in the data (von Neumann 1941). It is defined as:
.. math::
\eta = \frac{1}{(N-1)\sigma^2}
\sum_{i=1}^{N-1} (m_{i+1}-m_i)^2
The variability index should take a value close to 2 for a normal
distribution.
Although :math:`\eta` is a powerful index for quantifying variability
characteristics of a time series, it does not take into account unequal
sampling. Thus :math:`\eta^r` is defined as:
.. math::
\eta^e = \bar{w} \, (t_{N-1} - t_1)^2
\frac{\sum_{i=1}^{N-1} w_i (m_{i+1} - m_i)^2}
{\sigma^2 \sum_{i=1}^{N-1} w_i}
Where:
.. math::
w_i = \frac{1}{(t_{i+1} - t_i)^2}
Example:
.. code-block:: pycon
>>> fs = feets.FeatureSpace(only=['Eta_e'])
>>> features, values = fs.extract(**lc_normal)
>>> dict(zip(features, values))
{'Eta_e': 2.0028592616231866}
References
----------
.. [kim2014epoch] Kim, D. W., Protopapas, P., Bailer-Jones, C. A.,
Byun, Y. I., Chang, S. W., Marquette, J. B., & Shin, M. S. (2014).
The EPOCH Project: I. Periodic Variable Stars in the EROS-2 LMC
Database. arXiv preprint Doi:10.1051/0004-6361/201323252.
"""
data = ['magnitude', 'time']
features = ["Eta_e"]
[docs] def fit(self, magnitude, time):
w = 1.0 / np.power(np.subtract(time[1:], time[:-1]), 2)
w_mean = np.mean(w)
N = len(time)
sigma2 = np.var(magnitude)
S1 = sum(w * (magnitude[1:] - magnitude[:-1]) ** 2)
S2 = sum(w)
eta_e = (w_mean * np.power(time[N - 1] -
time[0], 2) * S1 / (sigma2 * S2 * N ** 2))
return {"Eta_e": eta_e}
