hMh dZddlZddlmZddlmZ ddeded ed ed ed ef d Z deded ed efdZ deded ed eeeffdZ dS)aeProject: PhiK - correlation analyzer library Created: 2018/09/05 Description: Implementation of incomplete beta function Authors: KPMG Advanced Analytics & Big Data team, Amstelveen, The Netherlands Redistribution and use in source and binary forms, with or without modification, are permitted according to the terms listed in the file LICENSE. N)gammaln)TupleHz>abxITMAXEPSreturncd}d}d}||z}|dz} |dz } d||z| z z } t|dzD]} t| dz} | | z}| || z z|z| |z||zzz }|||zz}| ||zz}|| z || zz|z| |z||zzz }|||zz}||| zz}|}||z }||z }||z }d} t||z |t|zkr|cStd|||)aContinued fraction form of the incomplete Beta function. Code translated from: Numerical Recipes in C. Example kindly taken from blog: https://malishoaib.wordpress.com/2014/04/15/the-beautiful-beta-functions-in-raw-python/ :param float a: a :param float b: b :param float x: x :param int ITMAX: max number of iterations, default is 5000. :param float EPS: epsilon precision parameter, default is 1e-7. :returns: continued fraction form :rtype: float g?z[a={0:f} or b={1:f} too large, or ITMAX={2:d} too small to compute incomplete beta function.)rangefloatabs ValueErrorformat)rrr r r azbmamqabqapqambziemtemdapbpappbppaolds L/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/phik/betainc.py contfractbetar%sv$ B B B a%C c'C c'C sQw} B 519   1q5\\2g !b&MA #)C!8 9 !b&[ !b&["fIr "Q &39S*A B1r6k1r6k #X #X 3Y  rDy>>C#b''M ) )III * ell q%    c|dkrdS|dkrdSt||zt|z t|z |tj|zz|tjd|z zz}||dz||zdzz kr*tj|t |||z|z }n/dtj|t ||d|z z|z z }|S)aEvaluation of incomplete beta function. Code translated from: Numerical Recipes in C. Here a, b > 0 and 0 <= x <= 1. This function requires contfractbeta(a,b,x, ITMAX = 200) Example kindly taken from blog: https://malishoaib.wordpress.com/2014/04/15/the-beautiful-beta-functions-in-raw-python/ :param float a: a :param float b: b :param float x: x :returns: incomplete beta function :rtype: float rr)rnplogexpr%)rrr lbetaps r$ incompbetar.Fs$ Avvq aq AENNWQZZ ''!** 4q26!99} Dq26RSVWRW==GX XEAEa!eai   F5MMM!Q22 2Q 6 u aAE : ::Q> > Hr&c F|dkrtj dfS|dkrdtj fSt||zt|z t|z |tj|zz|tjd|z zz}||dz||zdzz kr|tj|t |||z|z }|tjt |||ztj|z }tjd|z }ndtj|t ||d|z |z zz }tj|}|tjt ||d|z ztj|z }||fS)aWEvaluation of logarithm of incomplete beta function Logarithm of incomplete beta function is implemented to ensure sufficient precision for values very close to zero and one. Code translated from: Numerical Recipes in C. Here a, b > 0 and 0 <= x <= 1. This function requires contfractbeta(a,b,x, ITMAX = 200) Example kindly taken from blog: https://malishoaib.wordpress.com/2014/04/15/the-beautiful-beta-functions-in-raw-python/ :param float a: a :param float b: b :param float x: x :returns: tuple of log(incb) and log(1-incb) :rtype: tuple rrr()r)infrr*r+r%)rrr r,r-logplogqs r$log_incompbetar3est* Avvwz a26'z AENNWQZZ ''!** 4q26!99} Dq26RSVWRW==GX XEAEa!eai   F5MMM!Q22 2Q 6rvmAq!44555q Ava!e}} u q!QU!;!;a!?@ @vayyrvmAq!a%88999BF1IIE :r&)rr) __doc__numpyr) scipy.specialrtypingrrintr%r.r3r&r$r:s  !!!!!!CI// // /),/:?/ ////d % E e     >$e$$%$E%,4G$$$$$$r&