o Eb[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)nZrnr6/usr/lib/python3/dist-packages/scipy/stats/_ksstats.py_log_nfactorial_div_n_pow_n\s.rcCst|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^|dkr tdd|S||}|dkrtdd|Stt|}||}d|d}t||g}td|d}d||} t|} d} |D]} | | | d<| | } | | d| 9<qGtd|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}|dks||d|df}td|dD]}|||}t |tkr|t9}|t8}q|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]. rr?rrrN)Zaxis)rintr ceilzerosarangeemptymaxrangeZflipZeyeshapematmulabs_EP128_E128_EM128ldexp)r drZndkhmHZintmvwZfacjttiZHpwrnnexpntZHexpntrrrr _kolmogn_DMTWqs`      "&      r4c Cs|dkr| |d||d}}nLt|dd\}}|dkrN||dkr8|||d|||d}}n'|d||d||d|d}}n|d|d|||d}}t|ddt||fS)z0Compute the endpoints of the interval for row i.rrr)divmodrmin) r1r llceilfroundfj1j2Zip1div2Zip1mod2rrr_pomeranz_compute_j1j2s $,"r<c Cs||}tt|}d||}t|d|}|dkrdnd}|dkr&dnd}d|d} t| } t| } t| } d| d<d| d<d| d<d} ||d||dd||}}}td| D]&}| |d||| |<| |d||| |<| |d||| |<qdt| g}t| g}d|d<d\}}td||||\}}tdd|dD]}|}||}}||}}|dt|||||\}}|dks|d|dkr| }n|dr| n| }||d}|dkr:t |||||||d|}||}||d}|||||d|<dt |kr*t kr4nn|t 9}| t 8} |||}q|||}td|dD]}t|t krZ|t 9}| t 7} ||9}qH| dkrkt|| }t|d||}|S) z[Computes Pr(D_n <= d) using the Pomeranz recursion algorithm. Pomeranz (1974) [2] rrrrr)rrrN)rr Zfloorr6rr rr<fillZconvolverr&r$r%r#r'r) r xrtr7fgr8r9ZnpwrsZgpowerZ twogpowerZ onem2gpowerr3Zg_over_nZ two_g_over_nZone_minus_two_g_over_nr+ZV0ZV1ZV0sZV1sr:r;r1Zk1ZpwrsZln2convZ conv_startZconv_lenZansrrr_kolmogn_Pomeranzsl     (       ( "     rCc% 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}td}t t d |tj }t |ddD]G}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] rrrrrrrr@i`iZrrHiP i@)rr sqrt _PI_SQUARED_MIN_LOGexp_PI_FOUR_PI_SIXrrrpir ZpowerZarray_SQRT2PIr_SQRT3sumlen)%r r>rzZzsquaredZzthreeZzfourZzsixZqlogqZk1aZk1bZk2aZk2bZk2cZk3dZk3cZk3bZk3aZK0to3Zmaxkr)r+ZmsquaredZmfourZmsixZqpowerZcoeffsksZksquaredZsqrt3zZkspiZqpwersZk2extraZk3extraZ powers_of_nZKsumrrr_kolmogn_PelzGood"sl $     * racCsPt|r|St||ks|dkrtjS|dkrtdd|dS|dkr*tdd|dS||}|dkrr|dkr=tdd|dS|dkrWttd|dd|d|d}ntt||t d|d}t|d||dS||dkrdd||}td|||dS|dkrdt j ||}td|||dS||}|dkr|d krt ||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||ddkrt ||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]. rrrrDrrrg0q&?Trg w@g@g2@ig?gffffff?)r isnanrnanrprodrrVrr scipyspecialZsmirnovr4rCrra)r r>rr?ZprobZ nxsquaredrrrr_kolmognusX ,$  rhcsHtrStksdkrtjS|dks|dkrdS|}|dkr`|dkr,dSdkrDttddd|d}nttdtd|d}|ddS|dkrrdd|dS|dkrdt j j |S|d}t ||d}t |d|}fd d }t jj|||d d S) zvComputes the PDF for the two-sided Kolmogorov-Smirnov statistic. x must be of type float, n of type integer. rrrrrbrrg@cs t|SN)kolmogn)_xr rr_kks z_kolmogn_p.._kkrF)ZdxZorder)r rcrrdrerrVrr rfZstatsZksoneZpdfr6ZmiscZ derivative)r r>r?Zprddeltarmrrlr _kolmogn_ps. ((  rocstrStksdkrtjSdkrdS|dkr"dStttjd}|dkrB|ddSt t|d }|ddkrY|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 rrrrrRcst|Sri)rh)r>r rrrsz_kolmogni..g+=)Zxtol)r rcrrdrVr rfrgZloggammaZexpm1scuZ _kolmogcirSr6optimizeZbrentq)r rr_rnr>Zx1Z_frrpr _kolmognis$ $ rtc Cstj|||dgdtjtjtjgd}|D](\}}}}t|r$||d<qt||kr1td|tt|||d|d<q|jd}|S)aComputes the CDF for the two-sided Kolmogorov-Smirnov distribution. The two-sided Kolmogorov-Smirnov distribution has as its CDF Pr(D_n <= x), for a sample of size n drawn from a distribution with CDF F(t), where D_n &= sup_t |F_n(t) - F(t)|, and F_n(t) is the Empirical Cumulative Distribution Function of the sample. Parameters ---------- n : integer, array_like the number of samples x : float, array_like The K-S statistic, float between 0 and 1 cdf : bool, optional whether to compute the CDF(default=true) or the SF. Returns ------- cdf : ndarray CDF (or SF it cdf is False) at the specified locations. The return value has shape the result of numpy broadcasting n and x. N)Z op_dtypes.n is not integral: rDr) r nditerZfloat64Zbool_rcr ValueErrorrhoperands) r r>rit_nrk_cdfr^resultrrrrjs   rjcCsnt||dg}|D]%\}}}t|r||d<q t||kr&td|tt|||d<q |jd}|S)aComputes the PDF for the two-sided Kolmogorov-Smirnov distribution. Parameters ---------- n : integer, array_like the number of samples x : float, array_like The K-S statistic, float between 0 and 1 Returns ------- pdf : ndarray The PDF at the specified locations The return value has shape the result of numpy broadcasting n and x. N.rur)r rvrcrrwrorx)r r>ryrzrkr^r|rrrkolmognps   r}c Cst|||dg}|D]7\}}}}t|r||d<q t||kr(td||r0|d|fnd||f\}} tt||| |d<q |jd} | S)aComputes the PPF(or ISF) for the two-sided Kolmogorov-Smirnov distribution. Parameters ---------- n : integer, array_like the number of samples q : float, array_like Probabilities, float between 0 and 1 cdf : bool, optional whether to compute the PPF(default=true) or the ISF. Returns ------- ppf : ndarray PPF (or ISF if cdf is False) at the specified locations The return value has shape the result of numpy broadcasting n and x. N.rurr)r rvrcrrwrtrx) r r_rryrzZ_qr{r^Z_pcdfZ_psfr|rrrkolmogni7s    r~)T)&Znumpyr Z scipy.specialrfZscipy.special._ufuncsrgZ_ufuncsrrZ scipy.miscr%r'Z longdoubler$r&rSrYrZr r rUr[rTrWrXr rrrr4r<rCrarhrortrjr}r~rrrrs8C      K  T S<* %