a BCCfN@s&ddlZddlZddlmmZddlm Z dZ e e de Z e e de ZedejZedejZdZedZejdZejdZejd Zgd Zd d Zd dZd&ddZd'ddZddZd(ddZd)ddZ d*ddZ!ddZ"ddZ#d+d d!Z$d"d#Z%d,d$d%Z&dS)-N) _derivativei<)gSˆBgAAz?g}<ٰj_g#+K?g88CgJ?gllfgUUUUUU?cCs6d|}t|d|td|tt||S)N?r)nplog_LOG_2PIZpolyval_STIRLING_COEFFS)nZrnrP/var/www/html/django/DPS/env/lib/python3.9/site-packages/scipy/stats/_ksstats.py_log_nfactorial_div_n_pow_n]srcCst|ddS)z%clips a probability to range 0<=p<=1.r )r Zclip)prrr _clip_probgsrTcCst|||}t|S)z>Selects either the CDF or SF, and then clips to range 0<=p<=1.)r wherer)cdfprobZsfprobcdfrrrr_select_and_clip_problsrcCs`|dkrtdd|S||}|dkr0tdd|Stt|}||}d|d}t||g}td|d}d||} t|} d} |D],} | | | d<| | } | | d| 9<qtd|dd|d||} d| | | d<td|D](}| d||d||dd|f<q| |dddf<tj | dd |dddf<t t |d}|}d}d}|dkr|drt ||}||7}t ||}|d9}t ||d|dftkr|t}|t7}|d}ql||d|df}td|dD]2}|||}t |tkr|t9}|t8}q|dkrPt||}t|d||S) zComputes 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 r?rrrN)Zaxis)rintr ceilzerosarangeemptymaxrangeflipeyeshapematmulabs_EP128_E128_EM128ldexp)rdrndkhmHZintmvwZfacjttiZHpwrnnexpntZHexpntrrrr _kolmogn_DMTWrs\       "&          r8c Cs|dkr&| |d||d}}nt|dd\}}|dkr||dkrp|||d|||d}}q|d||d||d|d}}n"|d|d|||d}}t|ddt||fS)z0Compute the endpoints of the interval for row i.rrr)divmodr min) r5rllceilfroundfj1j2Zip1div2Zip1mod2rrr_pomeranz_compute_j1j2s $,"r@c Cs||}tt|}d||}t|d|}|dkrr?r5Zk1ZpwrsZln2convZ conv_startZconv_lenZansrrr_kolmogn_Pomeranzsj     (       ( "    rHc% Cs0|dkrtdd|dS|dkr,tdd|dSt||}|d|d|d|df\}}}}t d|}|tkrtdd|dSt|} | } td} d|d|} d|d |td} td d|d }td d |d }td|d|d }td|d|d}d|d|d}td}t t d |tj }t |ddD]}d|d }|d|d|d}}}t | d|}td| | || | ||||||||||g}||9}||7}q\|| 9}|t9}|t|d|d|dd|dg}tt d|} t|dd}|d}t|}tj |}| |} t|| }!|!ttd|9}!|d|!7<t|||||| }"|"ttd|9}"|d|"7<t |dtt|d}#||#}|s$|d9}|dd 7<t|}$|$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 rrrrrr@i`iZrrHiP i@)rr sqrt _PI_SQUARED_MIN_LOGexp_PI_FOUR_PI_SIXrrrpir!powerarray_SQRT2PIr_SQRT3sumlen)%rrCrzZzsquaredZzthreeZzfourZzsixZqlogqZk1aZk1bZk2aZk2bZk2cZk3dZk3cZk3bZk3aZK0to3Zmaxkr-r/ZmsquaredZmfourZmsixZqpowerZcoeffsksZksquaredZsqrt3zZkspiZqpwersZk2extraZk3extraZ powers_of_nZKsumrrr_kolmogn_PelzGood#sl $     * rhcCs`t|r|St||ks"|dkr(tjS|dkr>tdd|dS|dkrTtdd|dS||}|dkr|dkrztdd|dS|dkrttd|dd|d|d}n$tt||t d|d}t|d||dS||dkrdd||}td|||dS|dkrBdt j ||}td|||dS||}|dkr|d kr~t ||d d}t|d||dS|d krt||d d}t|d||dSdt j ||}td|||dS|s|d krdS|d krdt j ||}t|S|dkrd}n:|dkr@||ddkr@t ||d d}nt||d d}t|d||dS)zComputes the CDF(or SF) for the two-sided Kolmogorov-Smirnov statistic. x must be of type float, n of type integer. Simard & L'Ecuyer (2011) [7]. rr rrIrrrg0q&?Trg w@g@g2@ig?gffffff?)r isnanrnanrprodrr[rr scipyspecialZsmirnovr8rHrrh)rrCrrDZprobZ nxsquaredrrrr_kolmognvsX ,$       rocsFtrStks"dkr(tjS|dks8|dkr._kkrK)Zdxorder)r rjrrkrlrr[rr rmstatsZksoneZpdfr:r)rrCrDZprddeltartrrsr _kolmogn_ps. ((   rxcstrStks"dkr(tjSdkr8dS|dkrDdStttjd}|dkr|ddSt t|d }|ddkr|St t }t |dd}fdd}tjj|d|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 rrrWcst|Srp)ro)rCrrrr_fsz_kolmogni.._fg+=)Zxtol)r rjrrkr[r rmrnZloggammaexpm1scuZ _kolmogcirXr:optimizeZbrentq)rrrfrwrCx1rzrryr _kolmognis$ $ rc Cstj|||dgdtjtjtjgd}|D]P\}}}}t|rH||d<q(t||krbtd|tt|||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. N)Z op_dtypes.n is not integral: rIr) r nditerZfloat64Zbool_rjr ValueErrorrooperands) rrCrit_nrr_cdfreresultrrrrqs   rqcCsnt||dg}|D]J\}}}t|r2||d<qt||krLtd|tt|||d<q|jd}|S)aComputes 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.rr)r rrjrrrxr)rrCrrrrrerrrrkolmognps   rc Cst|||dg}|D]n\}}}}t|r6||d<qt||krPtd||r`|d|fn d||f\}} tt||| |d<q|jd} | S)aComputes 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.rrr)r rrjrrrr) rrfrrrZ_qrreZ_pcdfZ_psfrrrrkolmogni;s    r)T)T)T)T)T)T)T)'numpyr Z scipy.specialrmZscipy.special._ufuncsrnZ_ufuncsr|Zscipy._lib._finite_differencesrr(r*Z longdoubler'r)rXr^rar r rZrbrYr\r]r rrrr8r@rHrhrorxrrqrrrrrrDs6        K T S <* %