o ±Th«Nã@s&ddlZddlZddlmmZddlm Z dZ e  e  d¡e ¡Z e  e  d¡e ¡Ze dej¡Ze dej¡ZdZe d¡ZejdZejdZejd Zgd ¢Zd d „Zd d„Zd&dd„Zd&dd„Zdd„Zd&dd„Zd&dd„Z d&dd„Z!dd„Z"dd„Z#d&d d!„Z$d"d#„Z%d&d$d%„Z&dS)'éN)Ú _derivativeé€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©rúT/home/air/segue/gpt/backup/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_probgsrTcCst |||¡}t|ƒS)z>Selects either the CDF or SF, and then clips to range 0<=p<=1.)r Úwherer)ÚcdfprobÚsfprobÚcdfrrrrÚ_select_and_clip_problsrcCs^|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]. r rçà?rrréÿÿÿÿN)Úaxis)rÚintr ÚceilÚzerosÚarangeÚemptyÚmaxÚrangeÚflipÚeyeÚshapeÚmatmulÚabsÚ_EP128Ú_E128Ú_EM128Úldexp)rÚdrÚndÚkÚhÚmÚHÚintmÚvÚwÚfacÚjÚttÚiÚHpwrÚnnÚexpntÚHexpntrrrrÚ _kolmogn_DMTWrs`      "&  ö  €  rAc 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_j1j2½s $,"rKc Csê||}tt |¡ƒ}d||}t|d|ƒ}|dkrdnd}|dkr&dnd}d|d} t | ¡} t | ¡} t | ¡} d| d<d| d<d| d<d} ||d||dd||}}}td| ƒD]&}| |d||| |<| |d||| |<| |d||| |<qdt | g¡}t | g¡}d|d<d\}}td||||ƒ\}}tdd|dƒD]ˆ}|}||}}||}}| d¡t|||||ƒ\}}|dksÛ|d|dkrÞ| }n|drä| n| }||d}|dkr:t  ||||||…|d|…¡}||}||d}||||…|d|…<dt  |¡kr*t kr4nn|t 9}| t 8} |||}q²|||}td|dƒD]}t |¡t krZ|t 9}| t 7} ||9}qH| dkrkt || ¡}t|d||ƒ}|S) z[Computes Pr(D_n <= d) using the Pomeranz recursion algorithm. Pomeranz (1974) [2] r rrrr)rrrN)r r ÚfloorrCr$r&r"rKÚfillÚconvolver%r.r,r-r+r/r) rÚxrÚtrDÚfÚgrErFÚnpwrsÚgpowerÚ twogpowerÚ onem2gpowerr?Úg_over_nÚ two_g_over_nÚone_minus_two_g_over_nr4ÚV0ÚV1ÚV0sÚV1srGrHr<Úk1ÚpwrsÚln2ÚconvÚ conv_startÚconv_lenÚansrrrÚ_kolmogn_PomeranzÏsl     (       ( " €    rec% 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"r r!Úpir&ÚpowerÚarrayÚ_SQRT2PIr#Ú_SQRT3ÚsumÚlen)%rrOrÚzÚzsquaredÚzthreeÚzfourÚzsixÚqlogÚqÚk1aÚk1bÚk2aÚk2bÚk2cÚk3dÚk3cÚk3bÚk3aÚK0to3Úmaxkr2r4ÚmsquaredÚmfourÚmsixÚqpowerÚcoeffsÚksÚksquaredÚsqrt3zÚkspiÚqpwersÚk2extraÚk3extraÚ 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]. rr rrfréŒrrgã¤0ïq&è?Trg w@gš™™™™™@g2@i †gø?gffffffö?)r Úisnanr ÚnanrÚprodr#rxrr ÚscipyÚspecialÚsmirnovrArerr¢)rrOrrPÚprobÚ nxsquaredrrrrÚ_kolmognvsX ,$  r¬csDt 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|||d d S) zvComputes the PDF for the two-sided Kolmogorov-Smirnov statistic. x must be of type float, n of type integer. rr rrr£rrgð@cs tˆ|ƒS©N)Úkolmogn)Ú_x©rrrÚ_kkÖs z_kolmogn_p.._kkrh)ÚdxÚorder)r r¤r r¥r¦r#rxrr r§ÚstatsÚksoneÚpdfrCr)rrOrPÚprdÚdeltar±rr°rÚ _kolmogn_p²s. ((  r¹csþt 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 rr rrrtcstˆ|ƒˆSr­)r¬)rO©rrrrÚ_fósz_kolmogni.._fg›+¡†›„=)Úxtol)r r¤r r¥rxr r§r¨ÚloggammaÚexpm1ÚscuÚ _kolmogcirurCÚoptimizeÚbrentq)rrrˆr¸rOÚx1r»rrºrÚ _kolmogniÜs$ $ rÄc CsŒtj|||dgdgdtjtjtjgd}|D](\}}}}t |¡r&||d<qt|ƒ|kr3td|›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 :math:`D_n &= sup_t |F_n(t) - F(t)|`, and :math:`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. NÚ zerosize_ok)ÚflagsÚ op_dtypes.ún is not integral: rfr) r ÚnditerÚfloat64Úbool_r¤r Ú ValueErrorr¬Úoperands) rrOrÚitÚ_nr¯Ú_cdfr‚Úresultrrrr®ùsÿ   r®cCsnt ||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¤r rÌr¹rÍ)rrOrÎrÏr¯r‚rÑrrrÚkolmognps   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¤r rÌrÄrÍ) rrˆrrÎrÏÚ_qrÐr‚Ú_pcdfÚ_psfrÑrrrÚkolmogni;s    rÖ)T)'Únumpyr Ú scipy.specialr§Úscipy.special._ufuncsr¨Ú_ufuncsr¿Úscipy._lib._finite_differencesrr-r/Ú longdoubler,r.rur{r~r r rwrrvryrzrrrrrArKrer¢r¬r¹rÄr®rÒrÖrrrrÚs8C       K  T S<* %