_MhNddlZddlZddlmcmZddlm Z dZ ej ej de Z ej ej de ZejdejzZejdejzZdZejdZejdzZejdzZejd zZgd Zd Zd ZddZddZdZddZddZ ddZ!dZ"dZ#ddZ$dZ%ddZ&dS)N) _derivativei<)gSˆBgAAz?g}<ٰj_g#+K?g88CgJ?gllfgUUUUUU?cd|z }tj|dz |z tdz z|tjt||z zzS)N?r)nplog_LOG_2PIpolyval_STIRLING_COEFFS)nrns T/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/scipy/stats/_ksstats.py_log_nfactorial_div_n_pow_nr]sG QB 6!99Q;?XaZ '"rz:JBqD/Q/Q*Q QQc.tj|ddS)z%clips a probability to range 0<=p<=1.r )r clip)ps r _clip_probrgs 71c3  rTcLtj|||}t|S)z>Selects either the CDF or SF, and then clips to range 0<=p<=1.)r wherer)cdfprobsfprobcdfrs r_select_and_clip_probr ls! gv&&A a==rc8|dkrtdd|S||z}|dkrtdd|Sttj|}||z }d|zdz }tj||g}tjd|dz}d||zz } tj|} d} |D]"} | | | dz <| | z} | | dz xx| zcc<#td|zdz d|zd||zzz } d| z| z| d<td|D]}| d||z dz||dz d|f<| |dddf<tj | d |dddf<tj tj |d}|}d}d}|dkr|dzrtj ||}||z }tj ||}|dz}tj ||dz |dz ftkr|tz}|tz }|dz}|dk||dz |dz f}td|dzD];}||z|z }tj |t kr|tz}|tz}<|dkrtj||}t|d|z |S) zComputes the Kolmogorov CDF: Pr(D_n <= d) using the MTW approach to the Durbin matrix algorithm. Durbin (1968); Marsaglia, Tsang, Wang (2003). [1], [3]. r r?rrrN)axis)r intr ceilzerosarangeemptymaxrangeflipeyeshapematmulabs_EP128_E128_EM128ldexp)rdrndkhmHintmvwfacjttiHpwrnnexpntHexpntrs r _kolmogn_DMTWrFrs Cxx$S#s333 QB Syy$S#s333 BGBKKA BA A A !QA 9QA  D a4iA  A C !a% q !a%C QUS[!  a !AqD& (B 2X AbE 1a[[%%!a%!)}!a%&&!) AaaadGwqq!!!Ab!!!eH 6"(1++a. ! !D B E F q&& 6 9T1%%D VOE IaOO!  6!AE1q5L/ " "V + + KA eOF 1W q&& QUAE\A1a!e__ EAI 6!99v   KA UNE zz HQ   CE3 / //rcV|dkr| |z dz ||zdz }}not|dzd\}}|dkr=||dzkr||z |z dz ||z|zdz }}n3|dz |z |z dz ||zdz |zdz }}n|dz |z dz ||z|zdz }}t|dzdt||fS)z0Compute the endpoints of the interval for row i.rrr)divmodr*min) rArllceilfroundfj1j2ip1div2ip1mod2s r_pomeranz_compute_j1j2rQsAvvuq"u*q.B"!a%++ a<<!a%R%!+QVe^a-?B 1r)F2Q6" q8H58PST8TBq[2%)7R<&+@1+DB rAvq>>3r1:: %%rc||z}ttj|}d||z z}t|d|z }|dkrdnd}|dkrdnd}d|dzz} tj| } tj| } tj| } d| d<d| d<d| d<d} ||z d|z|z dd|zz |z }}}t d| D]>}| |dz |z|z | |<| |dz |z|z | |<| |dz |z|z | |<?tj| g}tj| g}d|d<d\}}td||||\}}t dd|zdzD]}|}||}}||}}|dt|||||\}}|dks |d|zdzkr| }n |dzr| n| }||z dz}|dkrtj |||z ||z |z|d|}||z }||z dz}||||z|d|<dtj |cxkr tkrnn|tz}| tz} ||z|z }|||z }t d|dzD]8}tj|tkr|tz}| tz } ||z}9| dkrtj|| }t!|d|z |}|S) z[Computes Pr(D_n <= d) using the Pomeranz recursion algorithm. Pomeranz (1974) [2] r rrr"r)rrrN)r%r floorrIr)r+r'rQfillconvolver*r3r1r2r0r4r ) rxrtrJfgrKrLnpwrsgpower twogpower onem2gpowerrDg_over_n two_g_over_none_minus_two_g_over_nr9V0V1V0sV1srMrNrAk1pwrsln2conv conv_startconv_lenanss r_kolmogn_Pomeranzrls}$ AA RXa[[  B q2vA AsQwAa%%QQQEs77aaF aLE Xe__FI(5//KF1IIaLKN E56qS!A#a%!ac'12lH 1e__II1q5MH,q0q  Q',6: ! $QU+.DDqH A 5'  B 5'  B BqEHC #Aq"eV < "9:D#JGGDbJBw{H J,A!ABByyM26"::&&&&&&&&&f (R-C QW+C 1a!e__ 6#;;   6MC UNE q zzhsE"" S3Y 4 4C Jrc |dkrtdd|S|dkrtdd|Stj||z}|dz|dz|dz|dzf\}}}}t dz |z }|tkrtdd|Stj|} | } tdz } d|zd|zz} d|zd |zz tzdz } t d d|zz zd z }td d |zz zd z }t d|zd|zzzd z }td|zd|zz zdz }d|zd|dzzz }tjd}ttj d |ztj z }t|ddD]w}d|zd z }|dz|dz|dz}}}tj | d|z}tjd| | |zz| | |zz||zz|||zz||zz||zzg}||z}||z }x|| z}|tz}|tj|d|zd|dzzd|dzzgz}tjt dz |z } tj|dd}|dz}t"|z}tj |z}| |z} tj|| z}!|!ttzd|zz z}!|dxx|!z cc<tj||z||z z|z| z}"|"ttzd|zz z}"|dxx|"z cc<tj |dztjt'|dz }#||#z}|s|dz}|dxxd z cc<t%|}$|$S)aPComputes the Pelz-Good approximation to Prob(Dn <= x) with 0<=x<=1. Start with Li-Chien, Korolyuk approximation: Prob(Dn <= x) ~ K0(z) + K1(z)/sqrt(n) + K2(z)/n + K3(z)/n**1.5 where z = x*sqrt(n). Transform each K_(z) using Jacobi theta functions into a form suitable for small z. Pelz-Good (1976). [6] rr rrrrr r@i`iZrr#HiP i@)r r sqrt _PI_SQUARED_MIN_LOGexp_PI_FOUR_PI_SIXr'r%r&pir+powerarray_SQRT2PIr(_SQRT3sumlen)%rrVrzzsquaredzthreezfourzsixqlogqk1ak1bk2ak2bk2ck3dk3ck3bk3aK0to3maxkr7r9msquaredmfourmsixqpowercoeffsksksquaredsqrt3zkspiqpwersk2extrak3extra powers_of_nKsums% r_kolmogn_PelzGoodr#s Cxx$S#37777Cxx$S#37777  QA$%qD!Q$1ad$:!HfeT  >>E  |a(*++A 4B  BQwH aZF 52:D (]FfX&''G {X%sV|44G !HHHHHHfftm 6AFJKKG {X%sTz22G !HHHHHH(1s7BIc%jj$9$9C$?@@K [E    aA  u::D Krc|tj|r|St||ks|dkr tjS|dkrt dd|S|dkrt dd|S||z}|dkr|dkrt dd|S|dkr:tjtjd|dzd|z zd|zdz z}n?tjt||tj d|zdz zz}t |d|z |S||dz kr dd|z |zz}t d|z ||S|dkr8dtj ||z}t d|z ||S||z}|dkr|d kr't||d }t |d|z |S|d kr't||d }t |d|z |Sdtj ||z}t d|z ||S|s@|d krdS|d kr2dtj ||z}t|S|dkrd}n7|dkr||dzzdkrt||d }nt!||d }t |d|z |S)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 rrnr"rrg0q&?Trg w@g@g2@ig?gffffff?)r isnanr%nanr prodr(rrr scipyspecialsmirnovrFrlrr)rrVrrWprob nxsquaredrs r_kolmognrvs x{{ 1vv{{a1ffv Cxx$S#37777Cxx$S#37777 AACxx 88(cs;;; ; 88729Q!,,A6!A#'BCCDD65a881rvac!e}};LLMMD$T3:3????AEzzC!Ga<$QXt====Cxx5=((A...$S4Z3????AICxx   A4000D(sTzsCCC C >>$Qt444D(sTzsCCC C5=((A...$S4Z3???? $   3   u},,Q222Dd## #D fQVs**1$///#Aqd333 #-S A A AArctjrStksdkr tjS|dks|dkrdS|z}|dkr|dkrdSdkr7tjtjddz zd|zdz z}nBtjtdz tjd|zdz zz}|dzdzzS|dz krdd|z dz zzzS|dkr(dtj j |zS|dz }t||dz z }t|d|z }fd }t|||d S) zvComputes the PDF for the two-sided Kolmogorov-Smirnov statistic. x must be of type float, n of type integer. rr r"rrrrg@c$t|SN)kolmogn)_xrs r_kkz_kolmogn_p.._kksq"~~rrp)dxorder)r rr%rrr(rrr rstatsksonepdfrIr)rrVrWprddeltars` r _kolmogn_prs  x{{ 1vv{{a1ffv Cxx166q AACxx 883 88'")Aq//S1W5QCDDCC&4Q771Q3"&QQRBSBS:SSTTCQwA~AEzzC!G1%%))Cxx5;$((A.... KE q3q5y ! !E sQw  E sA%q 1 1 11rctjrStksdkr tjSdkrdz S|dkrdStjtjt jdzz z }|dz kr |dz zdz Stj tj|dz z  }|ddz z kr|Stj tj z }t|ddz z }fd}t j|dz |dS) zeComputes the PPF/ISF of kolmogn. n of type integer, n>= 1 p is the CDF, q the SF, p+q=1 rr rrr|c*t|z Sr)r)rVrrs r_fz_kolmogni.._fs1~~!!rg+=)xtol)r rr%rrr rrloggammaexpm1scu _kolmogcir}rIoptimizebrentq)rrrrrVx1rs`` r _kolmognirs\  x{{ 1vv{{a1ffv Avv1u Avvs FBF1II 6 6qs ; ;;Q> ? ?E A~~a1$$ "&3--/ " ""AAAI~~ q  "'!** $B Rs1u  B"""""" > SUBU ; ;;rcrtj|||dgdgdtjtjtjg}|D]h\}}}}tj|r||d<!t ||krt d|tt ||||d<i|jd}|S)aComputes the CDF for the two-sided Kolmogorov-Smirnov distribution. The two-sided Kolmogorov-Smirnov distribution has as its CDF Pr(D_n <= x), for a sample of size n drawn from a distribution with CDF F(t), where :math:`D_n &= sup_t |F_n(t) - F(t)|`, and :math:`F_n(t)` is the Empirical Cumulative Distribution Function of the sample. Parameters ---------- n : integer, array_like the number of samples x : float, array_like The K-S statistic, float between 0 and 1 cdf : bool, optional whether to compute the CDF(default=true) or the SF. Returns ------- cdf : ndarray CDF (or SF it cdf is False) at the specified locations. The return value has shape the result of numpy broadcasting n and x. N zerosize_ok)flags op_dtypes.n is not integral: rnr#) r nditerfloat64bool_rr% ValueErrorroperands) rrVrit_nr_cdfrresults rrrs0 Aq#t$]O"BJ"*E G G GB11Ba 8B<< AcF  r77b==727788 8#b''24000# [_F Mrctj||dg}|D]e\}}}tj|r||d< t||krt d|t t|||d<f|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 rrr%rrr)rrVrrrrrs rkolmognprs" Aq$< B)) B 8B<< AcF  r77b==727788 8CGGR((# [_F MrcJtj|||dg}|D]z\}}}}tj|r||d<!t||krt d||r|d|z fnd|z |f\}} t t||| |d<{|jd} | S)aComputes the PPF(or ISF) for the two-sided Kolmogorov-Smirnov distribution. Parameters ---------- n : integer, array_like the number of samples q : float, array_like Probabilities, float between 0 and 1 cdf : bool, optional whether to compute the PPF(default=true) or the ISF. Returns ------- ppf : ndarray PPF (or ISF if cdf is False) at the specified locations The return value has shape the result of numpy broadcasting n and x. N.rrr#)r rrr%rrr) rrrrr_qrr_pcdf_psfrs rkolmognir;s& Aq#t$ % %B11Ba 8B<< AcF  r77b==727788 8$(8r1R4jjqtRj t3r77E400# [_F Mr)T)'numpyr scipy.specialrscipy.special._ufuncsr_ufuncsrscipy._lib._finite_differencesrr2r4 longdoubler1r3r}rrr rrrr~rrrrrr rFrQrlrrrrrrrrrrsH#########666666  -"-""E * * -"-""UF + + 271ru9   26!be)    eqj 5A: %1*III RRR    H0H0H0H0V&&&$QQQQhPPPPf9B9B9B9Bx'2'2'2T<<<:""""J:r