o Rŀg@s8dZddlmZddlmZddZddZdd Zd S) zpMethods to calculate p-values from a Chi-squared cumulative distribution function. for likelihood ratio tests. )exp)logcCsB|dkrtd|dkrtdd|}|d}dt||}|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)dfstatxalphaprobr G/var/www/html/myenv/lib/python3.10/site-packages/Bio/Phylo/PAML/chi2.pycdf_chi2srcCs|dkrt|}d}|dkr)d}|}|dkr"||9}|d7}|dks|}t| }d||}||dt||dd|d|d|d |S) 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 fzr r r_ln_gamma_function!s8   rcCs|}t|}d}d}d}d}d}d} d} d} d} |dkrdS|dks&|dkr(dSt|t|||} |dkr]||kr]d|}||d} d} d||d|| ddg}|d|d}n$d}d} |}| |kry|d7}| ||9} || 7}| |ksg|| |9}|S |d7}| d7} | d7} || } tdD]}| ||d| ||||d <q|d dkr|d |d }t||} | |kr|}n| ||krn(td D] }||d||<qt|d |krqtd D] }|||<qqd| |}|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 pgaccurateoverflowginrnabandiftermfactorpnir r rrDsn    &      rN)__doc__mathrrrrrr r r rs    #