allan deviaton

allan.py

import numpy as np

def allanVar(data, sf=1):
    '''
    calculates allan variance
    according to eq 8.13a in
    David W. Allan, John H. Shoaf and Donald Halford: Statistics of Time and Frequency Data Analysis,
    NBS Monograph 140, pages 151–204, 1974
    '''

    nd = np.array(data)
    
    # list of integration lengths
    # Note, this avoids using the full length!
    integration_lengths = np.unique(len(nd)/np.arange(1, len(nd)+1))[:-1]

    av = []
    for anint in integration_lengths:
        # Shorten array if necessary
        shorten_by = len(nd) % anint
        thend = nd
        if shorten_by != 0:
            thend = nd[:-shorten_by]
        
        # reshape and calculate mean
        x = thend.reshape(-1, anint).mean(axis=1)
        
        # Save the deviation
        av.append([anint*sf, ((x[1:] - x[:-1])**2).mean()/2])

    return np.array(av)

def allanDev(data, sf=1):
    alv = allanVar(data, sf)
    alv[:,1] = np.sqrt(alv[:,1])
    return alv