Prototype functions for my GSoC 16 project

prototype.py

from __future__ import division
import numpy as np
import stingray.lightcurve as lightcurve


def cross_covariance(lc1, lc2):
    """
    Compute the cross covariance of two lightcurves.
    
    Parameters
    ----------
    lc1 : Lightcurve object
        First light curve involved in the computation of cross covariance.
        
    lc2 : Lightcurve object
        Second light curve involved in the computation of cross covariance.
        
    Attributes
    ----------
    N : int
        Number of data points in the light curves.
        
    mean1 : float
        Mean of the count values of ``lc1``.
        
    mean2 : float
        Mean of the count values of ``lc2``.
        
    sigma : float
        Sum of the products of the difference of individual counts and their mean.
    """
    assert lc1.ncounts == lc2.ncounts, "Both lightcurves should have equal " \
                                       "number of data points."
    N = len(lc1.counts)
    mean1 = np.mean(lc1.counts)
    mean2 = np.mean(lc2.counts)
    sigma = np.sum([(lc1.counts[i] - mean1) * (lc2.counts[i] - mean2)
                    for i in range(N)])
    
    return sigma / (N - 1)


def _variance(lc):
    """
    Internal function to compute the variance of a lightcurve.
    """
    return np.var(lc.counts)


def cross_correlation(lc1, lc2):
    """
    Compute the cross-correlation of two lightcurves.

    Parameters
    ----------
    lc1 : Lightcurve object
        First light curve involved in the computation of cross covariance.
        
    lc2 : Lightcurve object
        Second light curve involved in the computation of cross covariance.
        
    Attributes
    ----------
    covar : float
        Cross-covaration of ``lc1`` and ``lc2``.
        
    norm_factor : float
        Square root of the product of variances of both lightcurve.
    """
    var1 = _variance(lc1)
    var2 = _variance(lc2)
    
    covar = cross_covariance(lc1, lc2)
    
    norm_factor = (var1 * var2)**0.5
    
    return covar / norm_factor


def auto_correlation(lc):
    """
    Compute the cross-autocorrelation of a lightcurve.
    """
    return cross_correlation(lc1, lc1)