a a[N@s"ddlZddlZddlmmZddlZdZ e e de Z e e de Z edejZedejZdZedZejdZejdZejdZgd Zd d Zd d Zd%ddZd&ddZddZd'ddZd(ddZd)ddZ ddZ!ddZ"d*dd Z#d!d"Z$d+d#d$Z%dS),Ni<)gSˆBgAAz?g}<ٰj_g#+K?g88CgJ?gllfgUUUUUU?cCs6d|}t|d|td|tt||S)N?r)nplog_LOG_2PIZpolyval_STIRLING_COEFFS)nZrnrd/Users/vegardjervell/Documents/master/model/venv/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_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]. rr?rrrN)Zaxis)rintr ceilzerosarangeemptymaxrangeZflipZeyeshapematmulabs_EP128_E128_EM128ldexp)r drndkhmHZintmvwZfacjttiZHpwrnnexpntZHexpntrrrr _kolmogn_DMTWqs\       "&          r5c 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) r2r llceilfroundfj1j2Zip1div2Zip1mod2rrr_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]. rrrrFrrrg0q&?Trg w@g@g2@ig?gffffff?)r isnanrnanrprodrrXrr scipyspecialZsmirnovr5rErre)r r@rrAZprobZ nxsquaredrrrr_kolmognusX ,$       rlcsJtrStks"dkr(tjS|dks8|dkr._kkrH)Zdxorder)r rgrrhrirrXrr rjstatsZksoneZpdfr7miscZ derivative)r r@rAZprddeltarqrrpr _kolmogn_ps. ((   rvcstrStks"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 rrrrrTcst|Srm)rl)r@r rrrz_kolmogni..g+=)Zxtol)r rgrrhrXr rjrkZloggammaexpm1scuZ _kolmogcirUr7optimizeZbrentq)r rrcrur@x1Z_frrwr _kolmognis$ $ r~c 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: rFr) r nditerZfloat64Zbool_rgr ValueErrorrloperands) r r@rit_nro_cdfrbresultrrrrns   rncCsnt||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 rrgrrrvr)r r@rrrorbrrrrkolmognps   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 rrgrrr~r) r rcrrrZ_qrrbZ_pcdfZ_psfrrrrkolmogni7s    r)T)T)T)T)T)T)T)&Znumpyr Z scipy.specialrjZscipy.special._ufuncsrkZ_ufuncsr{Z scipy.miscr%r'Z longdoubler$r&rUr[r^r r rWr_rVrYrZr rrrr5r=rErerlrvr~rnrrrrrrDs6       K T S <* %