U |evN@s2ddlZddlZddlmmZddlm Z dZ e e de Z e e de ZedejZedejZdZedZejdZejdZejd Zd d d d ddddgZddZddZd-ddZd.ddZddZd/ddZd0dd Z d1d!d"Z!d#d$Z"d%d&Z#d2d'd(Z$d)d*Z%d3d+d,Z&dS)4N) _derivativei<gSˆBgAAz?g}<ٰj_g#+K?g88CgJ?gllfgUUUUUU?cCs6d|}t|d|td|tt||S)N?r)nplog_LOG_2PIpolyval_STIRLING_COEFFS)nrnrQ/var/www/website-v5/atlas_env/lib/python3.8/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 clip)prrr _clip_probfsrTcCst|||}t|S)z>Selects either the CDF or SF, and then clips to range 0<=p<=1.)r wherer)cdfprobZsfprobcdfrrrr_select_and_clip_probksrcCs`|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)axis)rintr ceilzerosarangeemptymaxrangeflipeyeshapematmulabs_EP128_E128_EM128ldexp)rdrndkhmHZintmvwfacjttiZHpwrnnexpntZHexpntrrrr _kolmogn_DMTWqs\       "&          r=c 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) r:rllceilfroundfj1j2Zip1div2Zip1mod2rrr_pomeranz_compute_j1j2s $,"rEc Cs||}tt|}d||}t|d|}|dkrtdd|dS|dkrTtdd|dS||}|dkr|dkrztdd|dS|dkrttd|dd|d|d}n$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]. rr rrQrrrg0q&?Trg w@g@g2@ig?gffffff?)r isnanrnanrprodr"rcrr scipyspecialsmirnovr=rPrrq)rrIrrJprobZ nxsquaredrrrr_kolmognusX ,$       rzcsFtrStks"dkr(tjS|dks8|dkr._kkrS)dxorder)r rsrrtrur"rcrr rvstatsksonepdfr?r)rrIrJprddeltarrr~r _kolmogn_ps. ((   rcstrStks"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 rrr_cst|Sr{)rz)rIrrrrz_kolmogni..g+=)xtol)r rsrrtrcr rvrwloggammaexpm1scu _kolmogcir`r?optimizebrentq)rrrnrrIx1_frrr _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 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.n is not integral: rQr) r nditerfloat64bool_rsr ValueErrorrzoperands) rrIrit_nr}_cdfrmresultrrrr|s   r|cCsnt||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 rrsrrrr)rrIrrr}rmrrrrkolmognps   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 rrsrrrr) rrnrrrZ_qrrmZ_pcdfZ_psfrrrrkolmogni7s    r)T)T)T)T)T)T)T)'numpyr scipy.specialrvscipy.special._ufuncsrw_ufuncsrscipy._lib._finite_differencesrr,r. longdoubler+r-r`rfrir r rbrjrardrerrrrr=rErPrqrzrrr|rrrrrrDsD        K T S <* %