U ^{j'@slddlmZmZmZmZddlTddlmZddlm Z ddl Z d!dd Z d d Z d"d dZddZd#ddZedkrhddlZddZeejdkredenejddkrenejddkrednejddkren~ejddkr&eejdkrdn eejdZe enBejddkr>e n*ejddkrZee jned edS)$)absolute_importdivisionprint_functionunicode_literals)*)measures)datasetsN'c sddlm}ddddddd d d g }d d dddddddg }dd}|t|}|t|}g}tddD]}d|dtd|tfddt|D}tfddt|D}tfddt|D} |||| fqj|tdd|} |tdd|} |tdd|} | | | | d| tdddtdd| d | d!| dS)"u Recreates figure 2 of [w]_ comparing the reported values by Weron to the values obtained by the functions in this package. The experiment consists of n iterations where the hurst exponent of randomly generated gaussian noise is calculated. This is done with differing sequence lengths of 256, 512, 1024, ...., 65536. The average estimated hurst exponent over all iterations is plotted for the following configurations: * ``weron`` is the Anis-Lloyd-corrected Hurst exponent calculated by Weron * ``rs50`` is the Anis-Lloyd-corrected Hurst exponent calculated by Nolds with the same parameters as used by Weron * ``weron_raw`` is the uncorrected Hurst exponent calculated by Weron * ``rs50_raw`` is the uncorrected Hurst exponent calculated by Nolds with the same parameters as used by Weron * ``rsn`` is the Anis-Lloyd-corrected Hurst exponent calculated by Nolds with the default settings of Nolds The values reported by Weron are only measured from the plot in the PDF version of the paper and can therefore have some small inaccuracies. This function requires the package ``matplotlib``. References: .. [w] R. Weron, “Estimating long-range dependence: finite sample properties and confidence intervals,” Physica A: Statistical Mechanics and its Applications, vol. 312, no. 1, pp. 285–299, 2002. Kwargs: n (int): number of iterations of the experiment (Weron used 10000, but this takes a while) rNgE@g~j4*@g= ףp=4@gC5@gK7A6@g&18@g 8@gCL:@gʡ:@gI +d@gK7a@gJ +`@gsh|\@glY@gX9W@gp= ׳U@gB`"sT@gzGS@cSsd|ddS)Ng\(\?g/=@{Gz?)heightr r M/var/www/html/bwave/python/venv/lib/python3.8/site-packages/nolds/examples.py height_to_h6sz'weron_2002_figure2..height_to_hcs$g|]}tjtjjdddqS)sizepoly)fitnoldshurst_rsnprandomnormal.0_)lr r >sz&weron_2002_figure2..cs&g|]}tjtjjdddqS)rr)rnvalsrrr!r#r rr"Bscs(g|] }tjtjjddddqS)rrF)rr# correctedrrr$r rr"Fs)ZweronZ weron_rawrsnrs50rs50_rawzsequence lengthzestimated hurst exponent)matplotlib.pyplotpyplotrarrayrangearangemeanappendplotlegendZxticksxlabelylabelshow) npltZreportedZ reported_rawrdataer&r'r(linesrZrrr r$rweron_2002_figure2 sB$    r;cCsLddlm}ddtdD}|j|dd|d|d |dS) z Plots a histogram of values obtained for the hurst exponent of uniformly distributed white noise. This function requires the package ``matplotlib``. rNcSs$g|]}tjtjjddddqS)r rT)r%)rrrrrr r rr"]sz#plot_hurst_hist..d)Zbinsz esimated value of hurst exponentznumber of experiments)r)r*r,histr2r3r4)r6hsr r rplot_hurst_histTs    r@logisticc sddlm}ddd}|dkrbd}tdd d }tfd d |D}d d t||D}nh|dkrd}tddd }tfdd |D}tj||dkd}tj|t|dk<n t d|ddddddddfdd |D}fdd |D}t ||} t |dd| df||j d} | d||j||dddd} d} |j||d| d |j||d!| d ||tt|d"|j| | d#dd$d%|d&|||d'||f|jd(d)|dS)*u* Plots a bifurcation plot of the given map and superimposes the true lyapunov exponent as well as the estimates of the largest lyapunov exponent obtained by ``lyap_r`` and ``lyap_e``. The idea for this plot is taken from [ll]_. This function requires the package ``matplotlib``. References: .. [ll] Manfred Füllsack, "Lyapunov exponent", url: http://systems-sciences.uni-graz.at/etextbook/sw2/lyapunov.html Kwargs: maptype (str): can be either ``"logistic"`` for the logistic map or ``"tent"`` for the tent map. rNg?(rAr:rr cs$g|]}tjt|ddqSZfloat32)Zdtype)rfromiterr Z logistic_map)rr:r5x_startr rr"~szplot_lyap..cSs>g|]6\}}ttt|d||t|dkqS)r?)rr.logabswhere)rxr:r r rr"stentz$\mu$cs$g|]}tjt|ddqSrE)rrFr Ztent_map)rmurGr rr"s)rLzmaptype %s not recognizedr)emb_dimZ matrix_dimr=)rPZlagZmin_tsepZtrajectory_lencsg|]}ttj|fqSr )maxrlyap_erd)kwargs_er rr"scsg|]}tj|fqSr )rZlyap_rrS)kwargs_rr rr"szLyapunov exponent of the %s mapzb-ztrue lyap. exponent)labelzestimation using lyap_ezestimation using lyap_rz#00AAAA)colorrWz#AA00AAzg--rozbifurcation plot)alpharW)rzlyap. exp / %s(x, %s)best)loc)r)r*rr-r+ziprJnanrLErrorrepeatZreshapeshapetitler0ZzeroslenZylimr2r3r1r4) Zmaptyper6Znbifur param_nameZ param_rangeZ full_dataZlambdasZ lambdas_eZ lambdas_rZbifur_xZbifurZelabZrlabr )rUrVr5rHr plot_lyapcsR     (   rfcCs>ddl}d}ttj|d}|ddtjid|idS)z Runs a profiling test for the function ``lyap_e`` (mainly used for development) This function requires the package ``cProfile``. rNr rIz lyap_e(data)rRr7)cProfilerZcumsumrZrunctxrrR)rgr5r7r r r profilingsrhcCs ddlm}t|}tdt|d}tj||ddd}tj|ddd}tt |dd d }|t t||dd dk}tj||ddd}d d } | |dd|dd| |d } | |dd|dd| |d } | |dd|dd| |d } g} g}|dk rltj||ddd}| |dd|dd| |d } | } dg}| d|d|| | | | dddg|t|d|d|dgdddg}|D]\}}td||fq|dk rtd|d|dS)ay Creates a plot that compares the results of different choices for nvals for the function hurst_rs. Args: data (array-like of float): the input data from which the hurst exponent should be estimated Kwargs: nvals (array of int): a manually selected value for the nvals parameter that should be plotted in comparison to the default choices rNrrTr)r# debug_datar)rirZint32cSsdd|DS)NcSsg|]}tt|qSr )rrJrZ expected_rs)rr5r r rr"sz5hurst_compare_nvals..corr..r )r#r r rcorrsz!hurst_compare_nvals..corroZcustomzlog(n)zlog((R/S)_n - E[(R/S)_n])alldefaultZdivisorsdefdivz%s: %.3fz custom: %.3f)r)r*rZasarrayr-rdrrroundexpZastyperLr0r2r3r1r^printr4)r7r#r6Zn_allZdd_allZdd_defZn_defZn_divZdd_divrkZl_allZl_defZl_divZl_cstZt_cstZdd_cstZ labeled_datarWr r rhurst_compare_nvalss8  "&&& &  ""  rt__main__cCs<tdtdtdtdtdtdtddS)Nz options are:z lyapunov-logisticz lyapunov-tentz profilingz hurst-weron2z hurst-histz hurst-nvals)rsr r r r print_optionssrvrz*please tell me which tests you want to runzlyapunov-logisticz lyapunov-tentrNz hurst-weron2iz hurst-histz hurst-nvalsz#i do not know any test of that name)r )rA)N) __future__rrrrbuiltinsrrr numpyrr;r@rfrhrt__name__sysrvrdargvrsintr5Zbrown72r r r rs<   I P /  "