Xf4dZddlmZddlmZdZdZdZdS)zpMethods to calculate p-values from a Chi-squared cumulative distribution function. for likelihood ratio tests. )exp)logc|dkrtd|dkrtdd|z}|dz }dt||z }|S)z@Compute p-value, from distribution function and test statistics.zdf must be at least 1rz#The test statistic must be positive?g@) ValueError_incomplete_gamma)dfstatxalphaprobs 3lib/python3.11/site-packages/Bio/Phylo/PAML/chi2.pycdf_chi2rs^ Avv0111 axx>??? d A HE  E** *D Kc|dkrt|}d}|dkr,d}|}|dkr||z}|dz }|dk|}t| }d||zz }||dz t|zz|z dzd|zdz|zdz |zd z|z zS) aCompute the log of the gamma function for a given alpha (PRIVATE). Comments from Z. Yang: Returns ln(gamma(alpha)) for alpha>0, accurate to 10 decimal places. Stirling's formula is used for the central polynomial part of the procedure. Pike MC & Hill ID (1966) Algorithm 291: Logarithm of the gamma function. Communications of the Association for Computing Machinery, 9:684 rrrgdg?g48CgJ?gnlf?g=UUUUU?)rr)r r fzs r_ln_gamma_functionr!s zz A A1uu  !ee FA FA!ee  VVG QU A s7c!ff       !1$'88A =@Q QUV V     rcp|}t|}d}d}d}d}d}d} d} d} d} |dkrdS|dks|dkrdSt|t|z|z |z } |dkr5||kr/d|z }||zdz} d} d||dz|| zddg}|d|dz }n.d}d} |}| |kr|dz }| ||z z} || z }| |k|| |z z}|S |dz }| dz } | dz } || z} tdD]"}| ||dzz| ||zz ||d z<#|d dkr6|d |d z }t ||z } | |kr|}n | ||zkrn]td D]}||dz||<t |d |krtd D]}||xx|zcc<d| |zz }|S) a/Compute an incomplete gamma ratio (PRIVATE). Comments from Z. Yang:: Returns the incomplete gamma ratio I(x,alpha) where x is the upper limit of the integration and alpha is the shape parameter. returns (-1) if in error ln_gamma_alpha = ln(Gamma(alpha)), is almost redundant. (1) series expansion if alpha>x or x<=1 (2) continued fraction otherwise RATNEST FORTRAN by Bhattacharjee GP (1970) The incomplete gamma integral. Applied Statistics, 19: 285-287 (AS32) g:0yE>gꌠ9Y>)FrrNT)rrrrangeabs)r r pgaccurateoverflowginrnabandiftermfactorpnis rr r Dss A5!!AHH C B A A B C DAvvq1uuQr SVVa!# $ $F1uua E EAIAE1q5$ -ebem Xoo !GB AFND 4KCXoo vz  Q Q   Xq 3 3ABq1uI RU 2Bq1uII a5A::AABcBh--CX~~2 %%q  Aq1uIBqEE r!u:: q  A qEEEX EEEE'( fsl C JrN)__doc__mathrrrrr rrr0sr       FEEEEEr