M/Ph, dZddlZddlmZddlmZddlm Z ddl m Z m Z ddl m Z mZddlmZddlmZmZdd lmZd d gZd d gZd Ze eedZeeddZe eeZd6dZd7dZdZdZdZ dZ!dZ"dZ#dZ$d dgZ%d dgZ&d d gZ'gdZ(d dgZ)e*de$fde#fde"fde"fgZ+de&e'ffde&e(ffde%e'ffde%e)ffgZ,e,D]\Z-Z.e.\ZZe/d e/e-eee eed Z0eeed!Z1e-dd"d#kre+e-eZ2ne+e-eeZ2e/e0dd$e/e2dd$ee0e2dee1e2e2dz dd8d&Z3d9d(Z4d:d*Z5d+Z6d,ed,dfd-Z7e3Z8ee8dZ9e9:d.Z;e/e;dee8dZ<ee8dd/0Z=e4e8dZ>e4e8de8d?z Z@e/edde/e@dde d dgd gd1Ze/eedd2e/e jAedejBeejCe7eeeejCe7eeed/3ejCeeez"acovf_explicit..Js9DDDQ7DF7 R$Z00DDDrr)rrange)armar= acovfexplr<s ` @racovf_explicitrCEs= r2 & &BDDDDD%))DDDI rc:|d }|d}d|dzzd|z|zzd|dzz z g}|d||zz||zzd|dzz z tdD]"}|d}|||z#tj|S)Nr,r )rr?rarray)r@rAr5r4rho_lasts r acovf_arma11rLMs AA 1A q!tGAaCEMBq!tG $ %CJJ!A#!}bAg&''' 1XX2w 1T6 8C==rc|d }|d }tjd}d|dzz|dzz|d<| ||zz|d<| |d<|S)Nr,rErrrzeros)rAb1b2rIs r acovf_ma2rR`sd Q%B Q%B (2,,C"a%i"a%CFcBrEkCFSCF Jrcb|d }tjd}d|dzz|d<| |d<|S)Nr,rrErrN)rAr4rIs r acovf_ma1rTos= AA (2,,C!Q$hCFRCF Jrgg)r rg333333?ma1ma2arma11ar1)r=)lagsrErActjgd}tj||dz}tj|}t |}t |D]<}||tj|d|ddd|d|z||<=t ||D]7}||tj|||z |ddd|z||<8|||fS)N)g@gQ|g|?5^:@goŏg?)sizescalerG)rrHrandomnormalrOr/r?r9)NsigmatapsvuPls r ar_generatorrhs 8666 7 7D aucz22A  A D A 1XX44tbfQrrU44R4[$rr(333! 1QZZ33tbfQqs1uXddd^T222! a:rrGc|j|}tj|d|zdz |}tj||z|jd|}||z S)zReturns the autocorrelation of signal s at all lags. Adheres to the definition r(k) = E{s(n)s*(n-k)} where E{} is the expectation operator. rEr,)nr")r"N)shaperfftifft conjugatereal)sr"raSsxxs rautocorrrssh  A  1!AD ))A &++a oD+ 1 1 6rr :C q5Lrvalidctj|||tj|tj|z|jdzz S)zReturns the correlation between two ndarrays, by calling np.correlate in 'same' mode and normalizing the result by the std of the arrays and by their lengths. This results in a correlation = 1 for an auto-correlationrG)r correlatestdrk)rr2modes r norm_corrrysB \!Ad # #fQiiq !172;/13rc |j||fi|S)a9 call signature:: acorr(x, normed=True, detrend=detrend_none, usevlines=True, maxlags=10, **kwargs) Plot the autocorrelation of *x*. If *normed* = *True*, normalize the data by the autocorrelation at 0-th lag. *x* is detrended by the *detrend* callable (default no normalization). Data are plotted as ``plot(lags, c, **kwargs)`` Return value is a tuple (*lags*, *c*, *line*) where: - *lags* are a length 2*maxlags+1 lag vector - *c* is the 2*maxlags+1 auto correlation vector - *line* is a :class:`~matplotlib.lines.Line2D` instance returned by :meth:`plot` The default *linestyle* is None and the default *marker* is ``'o'``, though these can be overridden with keyword args. The cross correlation is performed with :func:`numpy.correlate` with *mode* = 2. If *usevlines* is *True*, :meth:`~matplotlib.axes.Axes.vlines` rather than :meth:`~matplotlib.axes.Axes.plot` is used to draw vertical lines from the origin to the acorr. Otherwise, the plot style is determined by the kwargs, which are :class:`~matplotlib.lines.Line2D` properties. *maxlags* is a positive integer detailing the number of lags to show. The default value of *None* will return all :math:`2 \mathrm{len}(x) - 1` lags. The return value is a tuple (*lags*, *c*, *linecol*, *b*) where - *linecol* is the :class:`~matplotlib.collections.LineCollection` - *b* is the *x*-axis. .. seealso:: :meth:`~matplotlib.axes.Axes.plot` or :meth:`~matplotlib.axes.Axes.vlines` For documentation on valid kwargs. **Example:** :func:`~matplotlib.pyplot.xcorr` above, and :func:`~matplotlib.pyplot.acorr` below. **Example:** .. plot:: mpl_examples/pylab_examples/xcorr_demo.py )xcorr)selfrkwargss rpltacorrr~s!x 4:a % %f % %%rTc nt|}|t|krtd|tj|}|tj|}tj||d} |r@| tjtj||tj||zz} ||dz }||ks|dkrtd|ztj| |dz} | |dz |z ||z} |rZ|j| dg| fi|} |j d i|} | dd | d d |j | | fi|} n?| dd | d d |j | | fi|\} d} | | | | fS) a call signature:: def xcorr(self, x, y, normed=True, detrend=detrend_none, usevlines=True, maxlags=10, **kwargs): Plot the cross correlation between *x* and *y*. If *normed* = *True*, normalize the data by the cross correlation at 0-th lag. *x* and y are detrended by the *detrend* callable (default no normalization). *x* and *y* must be equal length. Data are plotted as ``plot(lags, c, **kwargs)`` Return value is a tuple (*lags*, *c*, *line*) where: - *lags* are a length ``2*maxlags+1`` lag vector - *c* is the ``2*maxlags+1`` auto correlation vector - *line* is a :class:`~matplotlib.lines.Line2D` instance returned by :func:`~matplotlib.pyplot.plot`. The default *linestyle* is *None* and the default *marker* is 'o', though these can be overridden with keyword args. The cross correlation is performed with :func:`numpy.correlate` with *mode* = 2. If *usevlines* is *True*: :func:`~matplotlib.pyplot.vlines` rather than :func:`~matplotlib.pyplot.plot` is used to draw vertical lines from the origin to the xcorr. Otherwise the plotstyle is determined by the kwargs, which are :class:`~matplotlib.lines.Line2D` properties. The return value is a tuple (*lags*, *c*, *linecol*, *b*) where *linecol* is the :class:`matplotlib.collections.LineCollection` instance and *b* is the *x*-axis. *maxlags* is a positive integer detailing the number of lags to show. The default value of *None* will return all ``(2*len(x)-1)`` lags. **Example:** :func:`~matplotlib.pyplot.xcorr` above, and :func:`~matplotlib.pyplot.acorr` below. **Example:** .. plot:: mpl_examples/pylab_examples/xcorr_demo.py zx and y must be equal lengthrE)rxNr,z.maxlags must be None or strictly positive < %drmarkero linestyleNoner() r/ ValueErrorrrrvsqrtr9r.vlinesaxhline setdefaultplot)r|rr2normedr usevlinesmaxlagsr}NxcrYr5r4ds rpltxcorrrsp QB 3q66zz7888 1 A 1 A Q"""A 2 RWRVAq\\BF1aLL0 1 11q&"}}! )+-.// / 9gXgai ( (D "Q$w,r'z !"A  DKqc1 / / / / DL " "6 " "(C(((+v... DIdA ( ( ( ( (C(((+v... 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