o ÒtBh[Nã@s"ddlZddlZddlmmZddlZdZ e  e  d¡e ¡Z e  e  d¡e ¡Z e dej¡Ze dej¡ZdZe d¡ZejdZejdZejdZgd ¢Zd d „Zd d „Zd%dd„Zd%dd„Zdd„Zd%dd„Zd%dd„Zd%dd„Z dd„Z!dd„Z"d%dd „Z#d!d"„Z$d%d#d$„Z%dS)&éNé€ééi<ýÿÿééé)g˜SˆBž¿g¤A¤Az?g}<™Ù°j_¿g#ÿ+•K?g88C¿g  J?glÁlÁf¿gUUUUUUµ?cCs6d|}t |¡d|td|t t||¡S)Nçð?r)ÚnpÚlogÚ_LOG_2PIÚpolyvalÚ_STIRLING_COEFFS)ÚnÚrn©rúk/var/www/html/riverr-enterprise-integrations-main/venv/lib/python3.10/site-packages/scipy/stats/_ksstats.pyÚ_log_nfactorial_div_n_pow_n\s.rcCst |dd¡S)z%clips a probability to range 0<=p<=1.çr)r Úclip)ÚprrrÚ _clip_probfsrTcCst |||¡}t|ƒS)z>Selects either the CDF or SF, and then clips to range 0<=p<=1.)r Úwherer)ÚcdfprobÚsfprobÚcdfrrrrÚ_select_and_clip_probksrcCs^|dkr tdd|ƒS||}|dkrtdd|ƒStt |¡ƒ}||}d|d}t ||g¡}t d|d¡}d||} t |¡} d} |D]} | | | d<| | } | | d| 9<qGtd|ddƒ|d||} d| | | d<td|ƒD]}| d||d…||dd…|f<q|| |dd…df<tj | dd |ddd…f<t  t  |¡d¡}|}d}d}|dkrñ|drÈt  ||¡}||7}t  ||¡}|d9}t  ||d|df¡tkré|t}|t7}|d}|dksº||d|df}td|dƒD]}|||}t  |¡tkr|t9}|t8}q|dkr't ||¡}t|d||ƒS) z§Computes the Kolmogorov CDF: Pr(D_n <= d) using the MTW approach to the Durbin matrix algorithm. Durbin (1968); Marsaglia, Tsang, Wang (2003). [1], [3]. rrçà?rrréÿÿÿÿN)Úaxis)rÚintr ÚceilÚzerosÚarangeÚemptyÚmaxÚrangeÚflipÚeyeÚshapeÚmatmulÚabsÚ_EP128Ú_E128Ú_EM128Úldexp)rÚdrÚndÚkÚhÚmÚHÚintmÚvÚwÚfacÚjÚttÚiÚHpwrÚnnÚexpntÚHexpntrrrrÚ _kolmogn_DMTWqs`      "&  ö  €  r@c CsÖ|dkr| |d||d}}nLt|ddƒ\}}|dkrN||dkr8|||d|||d}}n'|d||d||d|d}}n|d|d|||d}}t|ddƒt||ƒfS)z0Compute the endpoints of the interval for row i.rrr)Údivmodr$Úmin) r;rÚllÚceilfÚroundfÚj1Új2Úip1div2Úip1mod2rrrÚ_pomeranz_compute_j1j2¼s $,"rJc Csê||}tt |¡ƒ}d||}t|d|ƒ}|dkrdnd}|dkr&dnd}d|d} t | ¡} t | ¡} t | ¡} d| d<d| d<d| d<d} ||d||dd||}}}td| ƒD]&}| |d||| |<| |d||| |<| |d||| |<qdt | g¡}t | g¡}d|d<d\}}td||||ƒ\}}tdd|dƒD]ˆ}|}||}}||}}| d¡t|||||ƒ\}}|dksÛ|d|dkrÞ| }n|drä| n| }||d}|dkr:t  ||||||…|d|…¡}||}||d}||||…|d|…<dt  |¡kr*t kr4nn|t 9}| t 8} |||}q²|||}td|dƒD]}t |¡t krZ|t 9}| t 7} ||9}qH| dkrkt || ¡}t|d||ƒ}|S) z[Computes Pr(D_n <= d) using the Pomeranz recursion algorithm. Pomeranz (1974) [2] rrrrr)rrrN)rr ÚfloorrBr#r%r!rJÚfillÚconvolver$r-r+r,r*r.r) rÚxrÚtrCÚfÚgrDrEÚnpwrsÚgpowerÚ twogpowerÚ onem2gpowerr>Úg_over_nÚ two_g_over_nÚone_minus_two_g_over_nr3ÚV0ÚV1ÚV0sÚV1srFrGr;Úk1ÚpwrsÚln2ÚconvÚ conv_startÚconv_lenÚansrrrÚ_kolmogn_PomeranzÎsl     (       ( " €    rdc% Cs.|dkr tdd|dS|dkrtdd|dSt |¡|}|d|d|d|df\}}}}t d|}|tkrAtdd|dSt |¡} | } td} d|d|} d|d |td} td d|d }td d |d }td|d|d }td|d|d}d|d|d}t d¡}t t  d |tj ¡ƒ}t |ddƒD]G}d|d }|d|d|d}}}t  | d|¡}t d| | || | ||||||||||g¡}||9}||7}q®|| 9}|t9}|t |d|d|dd|dg¡}t t d|¡} t |dd¡}|d}t|}tj |}| |} t || ¡}!|!ttd|9}!|d|!7<t |||||| ¡}"|"ttd|9}"|d|"7<t  |dt t|ƒ¡d¡}#||#}|s‘|d9}|dd 7<t|ƒ}$|$S)aPComputes the Pelz-Good approximation to Prob(Dn <= x) with 0<=x<=1. Start with Li-Chien, Korolyuk approximation: Prob(Dn <= x) ~ K0(z) + K1(z)/sqrt(n) + K2(z)/n + K3(z)/n**1.5 where z = x*sqrt(n). Transform each K_(z) using Jacobi theta functions into a form suitable for small z. Pelz-Good (1976). [6] rr©rrrrréérééé@iÄÿÿÿéÔé‡é`iâÿÿÿéZrréHéiPé iÜÿÿÿéØç@)rr ÚsqrtÚ _PI_SQUAREDÚ_MIN_LOGÚexpÚ_PI_FOURÚ_PI_SIXr!rr Úpir%ÚpowerÚarrayÚ_SQRT2PIr"Ú_SQRT3ÚsumÚlen)%rrNrÚzÚzsquaredÚzthreeÚzfourÚzsixÚqlogÚqÚk1aÚk1bÚk2aÚk2bÚk2cÚk3dÚk3cÚk3bÚk3aÚK0to3Úmaxkr1r3ÚmsquaredÚmfourÚmsixÚqpowerÚcoeffsÚksÚksquaredÚsqrt3zÚkspiÚqpwersÚk2extraÚk3extraÚ powers_of_nÚKsumrrrÚ_kolmogn_PelzGood"sl $    ý * r¡cCsPt |¡r|St|ƒ|ks|dkrtjS|dkrtdd|dS|dkr*tdd|dS||}|dkrr|dkr=tdd|dS|dkrWt t d|d¡d|d|d¡}nt t|ƒ|t  d|d¡¡}t|d||dS||dkr‰dd||}td|||dS|dkrŸdt j   ||¡}td|||dS||}|dkrá|d kr»t ||d d}t|d||dS|d krÏt||d d}t|d||dSdt j   ||¡}td|||dS|sú|d krédS|d krúdt j   ||¡}t|ƒS|dkrd}n|dkr||ddkrt ||d d}nt||d d}t|d||dS)z Computes the CDF(or SF) for the two-sided Kolmogorov-Smirnov statistic. x must be of type float, n of type integer. Simard & L'Ecuyer (2011) [7]. rrrreréŒrrgã¤0ïq&è?Trg w@gš™™™™™@g2@i †gø?gffffffö?)r ÚisnanrÚnanrÚprodr"rwrr ÚscipyÚspecialÚsmirnovr@rdrr¡)rrNrrOÚprobÚ nxsquaredrrrrÚ_kolmognusX ,$  r«csHt ˆ¡rˆStˆƒˆksˆdkrtjS|dks|dkrdSˆ|}|dkr`|dkr,dSˆdkrDt t dˆ¡dˆd|d¡}nt tˆƒˆdt d|d¡¡}|dˆdS|ˆdkrrdd|ˆdˆS|dkr€dt j j   |ˆ¡S|d}t ||dˆƒ}t |d|ƒ}‡fd d „}t jj|||d d S) zvComputes the PDF for the two-sided Kolmogorov-Smirnov statistic. x must be of type float, n of type integer. rrrrr¢rrgð@cs tˆ|ƒS©N)Úkolmogn)Ú_x©rrrÚ_kkÕs z_kolmogn_p.._kkrg)ÚdxÚorder)r r£rr¤r¥r"rwrr r¦ÚstatsÚksoneÚpdfrBÚmiscÚ derivative)rrNrOÚprdÚdeltar°rr¯rÚ _kolmogn_p±s. ((  rºcsþt ˆ¡rˆStˆƒˆksˆdkrtjSˆdkrdˆS|dkr"dSt t ˆ¡tj ˆd¡ˆ¡}|dˆkrB|dˆdSt  t |d¡ˆ¡ }|ddˆkrY|St   ˆ¡t  ˆ¡}t |ddˆƒ}‡‡fdd„}tjj|dˆ|dd S) zeComputes the PPF/ISF of kolmogn. n of type integer, n>= 1 p is the CDF, q the SF, p+q=1 rrrrrscstˆ|ƒˆSr¬)r«)rN©rrrrÚñsz_kolmogni..g›+¡†›„=)Úxtol)r r£rr¤rwr r¦r§ÚloggammaÚexpm1ÚscuÚ _kolmogcirtrBÚoptimizeÚbrentq)rrr‡r¹rNÚx1Ú_frr»rÚ _kolmogniÛs$ $ rÆc Csˆtj|||dgdtjtjtjgd}|D](\}}}}t |¡r$||d<qt|ƒ|kr1td|›ƒ‚tt|ƒ||d|d<q|jd}|S)aComputes the CDF for the two-sided Kolmogorov-Smirnov distribution. The two-sided Kolmogorov-Smirnov distribution has as its CDF Pr(D_n <= x), for a sample of size n drawn from a distribution with CDF F(t), where D_n &= sup_t |F_n(t) - F(t)|, and F_n(t) is the Empirical Cumulative Distribution Function of the sample. Parameters ---------- n : integer, array_like the number of samples x : float, array_like The K-S statistic, float between 0 and 1 cdf : bool, optional whether to compute the CDF(default=true) or the SF. Returns ------- cdf : ndarray CDF (or SF it cdf is False) at the specified locations. The return value has shape the result of numpy broadcasting n and x. N)Ú op_dtypes.ún is not integral: rer) r ÚnditerÚfloat64Úbool_r£rÚ ValueErrorr«Úoperands) rrNrÚitÚ_nr®Ú_cdfrÚresultrrrr­õsÿ   r­cCsnt ||dg¡}|D]%\}}}t |¡r||d<q t|ƒ|kr&td|›ƒ‚tt|ƒ|ƒ|d<q |jd}|S)aŒComputes the PDF for the two-sided Kolmogorov-Smirnov distribution. Parameters ---------- n : integer, array_like the number of samples x : float, array_like The K-S statistic, float between 0 and 1 Returns ------- pdf : ndarray The PDF at the specified locations The return value has shape the result of numpy broadcasting n and x. N.rÈr)r rÉr£rrÌrºrÍ)rrNrÎrÏr®rrÑrrrÚkolmognps   rÒc Cs”t |||dg¡}|D]7\}}}}t |¡r||d<q t|ƒ|kr(td|›ƒ‚|r0|d|fnd||f\}} tt|ƒ|| ƒ|d<q |jd} | S)aûComputes the PPF(or ISF) for the two-sided Kolmogorov-Smirnov distribution. Parameters ---------- n : integer, array_like the number of samples q : float, array_like Probabilities, float between 0 and 1 cdf : bool, optional whether to compute the PPF(default=true) or the ISF. Returns ------- ppf : ndarray PPF (or ISF if cdf is False) at the specified locations The return value has shape the result of numpy broadcasting n and x. N.rÈrr)r rÉr£rrÌrÆrÍ) rr‡rrÎrÏÚ_qrÐrÚ_pcdfÚ_psfrÑrrrÚkolmogni7s    rÖ)T)&Únumpyr Ú scipy.specialr¦Úscipy.special._ufuncsr§Ú_ufuncsrÀÚ scipy.miscr,r.Ú longdoubler+r-rtrzr}r r rvr~rurxryr rrrr@rJrdr¡r«rºrÆr­rÒrÖrrrrÚs8C      K  T S<* %