B 0d[N@s.ddlZddlZddlmmZddlZdZ e e de Z e e de Z edejZedejZdZedZejdZejdZejdZd d d d d dddgZddZddZd,ddZd-ddZddZd.ddZd/ddZd0d d!Z d"d#Z!d$d%Z"d1d&d'Z#d(d)Z$d2d*d+Z%dS)3Ni<gSˆBgAAz?g}<ٰj_g#+K?g88CgJ?gllfgUUUUUU?cCs6d|}t|d|td|tt||S)Ng?r)nplog_LOG_2PIZpolyval_STIRLING_COEFFS)nZrnr F/var/www/html/venv/lib/python3.7/site-packages/scipy/stats/_ksstats.py_log_nfactorial_div_n_pow_n\srcCst|ddS)z%clips a probability to range 0<=p<=1.gg?)rZclip)pr r r _clip_probfsrTcCst|||}t|S)z>Selects either the CDF or SF, and then clips to range 0<=p<=1.)rwherer)cdfprobZsfprobcdfrr r r_select_and_clip_probksrcCsp|dkrtdd|S||}|dkr0tdd|Stt|}||}d|d}t||g}td|d}d||} t|} d} x4|D],} | | | d<| | } | | d| 9<qWtd|dd|d||} d| | | d<x6td|D](}| d||d||dd|f<qW| |dddf<tj | dd |dddf<t t |d}|}d}d}xz|dkr|drt ||}||7}t ||}|d9}t ||d|dftkr|t}|t7}|d}qvW||d|df}xDtd|dD]2}|||}t |tkr|t9}|t8}qW|dkr`t||}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]. g?gg?rrrN)Zaxis)rintrceilzerosarangeemptymaxrangeflipeyeshapematmulabs_EP128_E128_EM128ldexp)r drndkhmHZintmvwZfacjttiZHpwrnnexpntZHexpntrr r r _kolmogn_DMTWqs\        "(        r4c 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)divmodrmin) r1r llceilfroundfj1j2Zip1div2Zip1mod2r r r_pomeranz_compute_j1j2s $,"r<c Cs||}tt|}d||}t|d|}|dkrtdd|dS|dkrTtdd|dS||}|dkr|dkrztdd|dS|dkrttd|dd|d|d}n$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]. rg?g)rg?rrg0q&?Trg w@g@g2@ig?gffffff?)risnanrnanrprodrrUrr scipyspecialZsmirnovr4rDrrb)r r?rr@ZprobZ nxsquaredrr r r_kolmognusX ,$       ricsJtrStks"dkr(tjS|dks8|dkr._kkrF)Zdxorder)rrdrrerfrrUrr rgstatsZksoneZpdfr6miscZ derivative)r r?r@Zprddeltarlr )r r _kolmogn_ps. ((   rqcstrStks"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 rg?rrg@cst|S)N)ri)r?)r rr rz_kolmogni..g+=)Zxtol)rrdrrerUr rgrhZloggammaexpm1scuZ _kolmogcirRr6optimizeZbrentq)r rr`rpr?x1_fr )r rr _kolmognis$ $ ryc Cstj|||dgdtjtjtjgd}xX|D]P\}}}}t|rJ||d<q*t||krdtd|tt|||d|d<q*W|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)Z op_dtypes.zn is not integral: )rr) rnditerZfloat64Zbool_rdr ValueErrorrioperands) r r?rit_nrk_cdfr_resultr r rrjs   rjcCsrt||dg}xR|D]J\}}}t|r4||d<qt||krNtd|tt|||d<qW|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.zn is not integral: r)rrzrdrr{rqr|)r r?r}r~rkr_rr r rkolmognps   rc Cst|||dg}xv|D]n\}}}}t|r8||d<qt||krRtd||rb|d|fn d||f\}} tt||| |d<qW|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.zn is not integral: rr)rrzrdrr{ryr|) r r`rr}r~Z_qrr_Z_pcdfZ_psfrr r rkolmogni7s    r)T)T)T)T)T)T)T)&numpyrZ scipy.specialrgZscipy.special._ufuncsrhZ_ufuncsruZ scipy.miscr$r&Z longdoubler#r%rRrXr[r r rTr\rSrVrWr rrrr4r<rDrbrirqryrjrrr r r rDs<       K T S <* %