ó nTMc@s dZddlmZddlmZddlmZddlmZddl Z ddd„ƒYZ d e fd „ƒYZ d „Z d „Z ed krddlZd„ZddlmZddlmZddlmZddlmZddlmZdZeejdƒZejeƒejdeƒdee eƒƒdZ!e!dee eƒƒdZ!e de!eƒZ"e"j#GHe"j$ƒGHe"j%dƒZ&eefee!ƒƒd Z'e"j(dƒZ)e"j*ejdddƒƒZ+e"j,ƒGe"j-ƒdƒGe)j.ƒGHee)ƒndS( s0 Auto-regressive model for stochastic processes iÿÿÿÿ(tInterpolatingFunction(t Polynomial(tRationalFunction(tNNtAutoRegressiveModelcBsteZdZdd„Zd„Zd„Zd„Zd„Zd„Zd„Z d „Z d „Z d „Z d „Z RS( s’Auto-regressive model for stochastic process This implementation uses the Burg algorithm to obtain the coefficients of the AR model. icCs9||_||_d|_|j|ƒ|j|ƒdS(s @param order: the order of the model @type order: C{int} @param data: the time series @type data: sequence of C{float} or C{complex} @param delta_t: the sampling interval for the time series @type delta_t: C{float} N(tordertdelta_ttNonet_polest_findCoefficientst_setTrajectory(tselfRtdataR((s:C:\Python27\Lib\site-packages\Scientific\Signals\Models.pyt__init__s    c Cs£|}|}tjdgƒ}g}tjjt|ƒdƒt|ƒ}||_xt|jƒD]ñ}|d}|d } dtjj|tj | ƒƒtjj|tj |ƒ| tj | ƒƒ} |j | ƒ|| | }| tj | ƒ|}tj |dgfƒ}|| tj |ddd…ƒ}|dt| ƒd}qcW||jdd… |_ tj|ƒ|_ ||_tj|ƒ|_dS(Ngð?iiiÿÿÿÿg@gi(RtarraytaddtreducetabstlentvariancetrangeRt conjugatetappendt concatenatetcoefftparcortsigsqtsqrttsigma( R R tetbtaRRtrtertbrtg((s:C:\Python27\Lib\site-packages\Scientific\Signals\Models.pyR (s*&    1 $ cCstj||j ƒ|_dS(N(tcopyRt trajectory(R R ((s:C:\Python27\Lib\site-packages\Scientific\Signals\Models.pyR AscCsAtjj|j|jƒ}|jd|jd*||jd<|S(s` Calculates the linear prediction of the next step in the series. This step is appended internally to the current trajectory, making it possible to call this method repeatedly in order to obtain a sequence of predicted steps. @returns: the predicted step @rtype: C{float} or C{complex} iiÿÿÿÿ(RRRRR%(R tnext((s:C:\Python27\Lib\site-packages\Scientific\Signals\Models.pyt predictStepDs  cCs“d}xRtdt|jƒdƒD]4}||j| tjd||j|ƒ}q#Wd|j|j|tj|ƒj}t |f|ƒS(sÿ @param omega: the angular frequencies at which the spectrum is to be evaluated @type omega: C{Numeric.array} of C{float} @returns: the frequency spectrum of the process @rtype: C{Numeric.array} of C{float} gð?iyð¿gà?( RRRRtexpRRRtrealR(R tomegatsumtits((s:C:\Python27\Lib\site-packages\Scientific\Signals\Models.pytspectrumSs #2(cCs¿|jdkr¸ddlm}t|jƒ}|dkrI|j|_q¸tj||f|jƒ}tj|dƒ|dd…dd…f<|j|dd…df<||ƒ|_n|jS(s{ @returns: the poles of the model in the complex M{z}-plane @rtype: C{Numeric.array} of C{complex} iÿÿÿÿ(t eigenvaluesiN( RRt Scientific.LAR/RRRtzeros_sttidentity(R R/tnR((s:C:\Python27\Lib\site-packages\Scientific\Signals\Models.pytpolesas )c Cs±|jƒ}tj|ƒ}d}tj|jd||jdƒ}x tt|ƒƒD]õ}||}tjj||| ƒtjj|||dƒtjj|d|ƒ}y||||}WqXt k rLtj |j tj ƒ} xDtt|ƒƒD]0}y|||| |RKtmemttime((s:C:\Python27\Lib\site-packages\Scientific\Signals\Models.pytmemoryFunctionÑs ' cCs^|jƒ}tj|ƒ}tj|jdƒ}tj|jftjƒ}x•t|jƒD]„}||}|j||jd| tj j ||| ƒtj j |||dƒtj j |d|ƒ|j || s< ê1     8  %