initial import of classes for automatic picking purposes [just imported by me; module has originally been written by Ludger Küperkoch]
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pylot/core/pick/CharFuns.py
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pylot/core/pick/CharFuns.py
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# -*- coding: utf-8 -*-
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"""
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Created Oct/Nov 2014
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Implementation of the Characteristic Functions (CF) published and described in:
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Kueperkoch, L., Meier, T., Lee, J., Friederich, W., & EGELADOS Working Group, 2010:
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Automated determination of P-phase arrival times at regional and local distances
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using higher order statistics, Geophys. J. Int., 181, 1159-1170
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Kueperkoch, L., Meier, T., Bruestle, A., Lee, J., Friederich, W., & EGELADOS
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Working Group, 2012: Automated determination of S-phase arrival times using
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autoregressive prediction: application ot local and regional distances, Geophys. J. Int.,
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188, 687-702.
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:author: MAGS2 EP3 working group
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"""
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import numpy as np
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from obspy.core import Stream
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class CharacteristicFunction(object):
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'''
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SuperClass for different types of characteristic functions.
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'''
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def __init__(self, data, cut, t2, order, t1=None, fnoise=0.001):
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'''
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Initialize data type object with information from the original
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Seismogram.
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:param: data
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:type: `~obspy.core.stream.Stream`
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:param: cut
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:type: tuple
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:param: t2
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:type: float
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:param: order
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:type: int
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:param: t1
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:type: float (optional, only for AR)
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:param: fnoise
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:type: float (optional, only for AR)
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'''
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assert isinstance(data, Stream), "%s is not a Stream object" % str(data)
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self.orig_data = data[0]
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self.dt = self.orig_data.stats.delta
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self.setCut(cut)
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self.setTime1(t1)
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self.setTime2(t2)
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self.setOrder(order)
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self.setFnoise(fnoise)
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self.calcCF(self.getDataArray())
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self.arpara = np.array([])
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self.xpred = np.array([])
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def __str__(self):
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return '''\n\t{name} object:\n
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Cut:\t\t{cut}\n
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t1:\t{t1}\n
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t2:\t{t2}\n
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Order:\t\t{order}\n
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Fnoise:\t{fnoise}\n
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'''.format(name=type(self).__name__,
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cut=self.getCut(),
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t1=self.getTime1(),
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t2=self.getTime2(),
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order=self.getOrder(),
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fnoise=self.getFnoise())
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def getCut(self):
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return self.cut
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def setCut(self, cut):
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self.cut = cut
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def getTime1(self):
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return self.t1
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def setTime1(self, t1):
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self.t1 = t1
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def getTime2(self):
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return self.t2
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def setTime2(self, t2):
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self.t2 = t2
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def getOrder(self):
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return self.order
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def setOrder(self, order):
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self.order = order
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def getIncrement(self):
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return self.dt
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def getFnoise(self):
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return self.fnoise
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def setFnoise(self, fnoise):
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self.fnoise = fnoise
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def getCF(self):
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return self.cf
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def getDataArray(self, cut=None):
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'''
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If cut times are given, time series is cut from cut[0] (start time)
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till cut[1] (stop time) in order to calculate CF for certain part
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only where you expect the signal!
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input: cut (tuple) ()
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cutting window
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'''
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if cut is not None:
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if self.cut[0] == 0:
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start = 0
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else:
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start = self.cut[0] / self.dt
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stop = self.cut[1] / self.dt
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data = self.orig_data.data[start:stop]
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return data
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return self.orig_data.data
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def calcCF(self, data=None):
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self.cf = data
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def arDet(self, data, order, rind, ldet):
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pass
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def arPred(self, data, arpara, rind, lpred):
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pass
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class AICcf(CharacteristicFunction):
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'''
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Function to calculate the Akaike Information Criterion (AIC) after
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Maeda (1985).
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:param: data, time series (whether seismogram or CF)
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:type: tuple
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Output: AIC function
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'''
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def calcCF(self, data):
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print 'Calculating AIC ...'
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xnp = self.getDataArray()
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datlen = len(xnp)
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k = np.arange(1, datlen)
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cf = np.zeros(datlen)
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cumsumcf = np.cumsum(np.power(xnp, 2))
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i = np.where(cumsumcf == 0)
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cumsumcf[i] = np.finfo(np.float64).eps
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cf[k] = ((k - 1) * np.log(cumsumcf[k] / k) + (datlen - k + 1) *
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np.log((cumsumcf[datlen - 1] -
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cumsumcf[k - 1]) / (datlen - k + 1)))
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cf[0] = cf[1]
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inf = np.isinf(cf)
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ff = np.where(inf == 'True')
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if len(ff) >= 1:
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cf[ff] = 0
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self.cf = cf - np.mean(cf)
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class HOScf(CharacteristicFunction):
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'''
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Function to calculate skewness (statistics of order 3) or kurtosis
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(statistics of order 4), using one long moving window, as published
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in Kueperkoch et al. (2010).
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'''
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def calcCF(self, data):
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xnp = self.getDataArray(self.getCut())
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if self.getOrder() == 3: # this is skewness
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print 'Calculating skewness ...'
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y = np.power(xnp, 3)
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y1 = np.power(xnp, 2)
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elif self.getOrder() == 4: # this is kurtosis
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print 'Calculating kurtosis ...'
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y = np.power(xnp, 4)
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y1 = np.power(xnp, 2)
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# Initialisation
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# t2: long term moving window
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ilta = round(self.getTime2() / self.getIncrement())
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lta = y[0]
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lta1 = y1[0]
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# moving windows
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LTA = np.zeros(len(xnp))
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for j in range(3, len(xnp)):
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if j <= ilta:
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lta = (y[j] + lta * (j - 1)) / j
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lta1 = (y1[j] + lta1 * (j - 1)) / j
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else:
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lta = (y[j] - y[j - ilta]) / ilta + lta
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lta1 = (y1[j] - y1[j - ilta]) / ilta + lta1
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# define LTA
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if self.getOrder() == 3:
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LTA[j] = lta / np.power(lta1, 1.5)
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elif self.getOrder() == 4:
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LTA[j] = lta / np.power(lta1, 2)
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LTA[0:3] = 0
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self.cf = LTA
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class ARZcf(CharacteristicFunction):
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def calcCF(self, data):
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print 'Calculating AR-prediction error from single trace ...'
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xnp = self.getDataArray(self.getCut())
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# some parameters needed
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# add noise to time series
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xnoise = xnp + np.random.normal(0.0, 1.0, len(xnp)) * self.getFnoise() * max(abs(xnp))
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tend = len(xnp)
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# Time1: length of AR-determination window [sec]
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# Time2: length of AR-prediction window [sec]
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ldet = int(round(self.getTime1() / self.getIncrement())) # length of AR-determination window [samples]
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lpred = int(np.ceil(self.getTime2() / self.getIncrement())) # length of AR-prediction window [samples]
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cf = []
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step = ldet + self.getOrder() - 1
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for i in range(ldet + self.getOrder() - 1, tend - lpred + 1):
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if i == step:
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'''
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In order to speed up the algorithm AR parameters are kept for time
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intervals of length lpred
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'''
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# determination of AR coefficients
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self.arDet(xnoise, self.getOrder(), i - ldet, i)
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step = step + lpred
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# AR prediction of waveform using calculated AR coefficients
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self.arPred(xnp, self.arpara, i + 1, lpred)
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# prediction error = CF
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err = np.sqrt(np.sum(np.power(self.xpred[i:i + lpred] - xnp[i:i + lpred], 2)) / lpred)
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cf.append(err)
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# convert list to numpy array
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cf = np.asarray(cf)
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self.cf = cf
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def arDet(self, data, order, rind, ldet):
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'''
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Function to calculate AR parameters arpara after Thomas Meier (CAU), published
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in Kueperkoch et al. (2012). This function solves SLE using the Moore-
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Penrose inverse, i.e. the least-squares approach.
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:param: data, time series to calculate AR parameters from
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:type: array
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:param: order, order of AR process
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:type: int
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:param: rind, first running summation index
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:type: int
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:param: ldet, length of AR-determination window (=end of summation index)
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:type: int
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Output: AR parameters arpara
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'''
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# recursive calculation of data vector (right part of eq. 6.5 in Kueperkoch et al. (2012)
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rhs = np.zeros(self.getOrder())
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for k in range(0, self.getOrder()):
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for i in range(rind, ldet):
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rhs[k] = rhs[k] + data[i] * data[i - k]
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# recursive calculation of data array (second sum at left part of eq. 6.5 in Kueperkoch et al. 2012)
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A = np.array([[0, 0], [0, 0]])
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for k in range(1, self.getOrder() + 1):
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for j in range(1, k + 1):
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for i in range(rind, ldet):
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ki = k - 1
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ji = j - 1
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A[ki, ji] = A[ki, ji] + data[i - ji] * data[i - ki]
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A[ji, ki] = A[ki, ji]
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# apply Moore-Penrose inverse for SVD yielding the AR-parameters
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self.arpara = np.dot(np.linalg.pinv(A), rhs)
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def arPred(self, data, arpara, rind, lpred):
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'''
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Function to predict waveform, assuming an autoregressive process of order
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p (=size(arpara)), with AR parameters arpara calculated in arDet. After
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Thomas Meier (CAU), published in Kueperkoch et al. (2012).
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:param: data, time series to be predicted
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:type: array
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:param: arpara, AR parameters
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:type: float
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:param: rind, first running summation index
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:type: int
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:param: lpred, length of prediction window (=end of summation index)
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:type: int
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Output: predicted waveform z
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'''
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# be sure of the summation indeces
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if rind < len(arpara) + 1:
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rind = len(arpara) + 1
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if rind > len(data) - lpred + 1:
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rind = len(data) - lpred + 1
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if lpred < 1:
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lpred = 1
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if lpred > len(data) - 1:
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lpred = len(data) - 1
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z = np.append(data[0:rind], np.zeros(lpred))
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for i in range(rind, rind + lpred):
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for j in range(1, len(arpara) + 1):
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ji = j - 1
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z[i] = z[i] + arpara[ji] * z[i - ji]
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self.xpred = z
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class ARHcf(CharacteristicFunction):
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pass
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class AR3Ccf(CharacteristicFunction):
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pass
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