Package Bio :: Package Phylo :: Package PAML :: Module chi2
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Source Code for Module Bio.Phylo.PAML.chi2

  1  # Copyright (C) 2011 by Brandon Invergo (b.invergo@gmail.com) 
  2  # This code is part of the Biopython distribution and governed by its 
  3  # license. Please see the LICENSE file that should have been included 
  4  # as part of this package. 
  5  # 
  6  # This code is adapted (with permission) from the C source code of chi2.c, 
  7  # written by Ziheng Yang and included in the PAML software package: 
  8  # http://abacus.gene.ucl.ac.uk/software/paml.html 
  9   
 10  from math import log, exp 
 11   
 12   
13 -def cdf_chi2(df, stat):
14 if df < 1: 15 raise ValueError("df must be at least 1") 16 if stat < 0: 17 raise ValueError("The test statistic must be positive") 18 x = 0.5 * stat 19 alpha = df / 2.0 20 prob = 1 - _incomplete_gamma(x, alpha) 21 return prob
22 23
24 -def _ln_gamma_function(alpha):
25 """Compute the log of the gamma function for a given alpha. 26 27 Comments from Z. Yang: 28 Returns ln(gamma(alpha)) for alpha>0, accurate to 10 decimal places. 29 Stirling's formula is used for the central polynomial part of the procedure. 30 Pike MC & Hill ID (1966) Algorithm 291: Logarithm of the gamma function. 31 Communications of the Association for Computing Machinery, 9:684 32 """ 33 if alpha <= 0: 34 raise ValueError 35 x = alpha 36 f = 0 37 if x < 7: 38 f = 1 39 z = x 40 while z < 7: 41 f *= z 42 z += 1 43 x = z 44 f = -log(f) 45 z = 1 / (x * x) 46 return f + (x - 0.5) * log(x) - x + .918938533204673 + \ 47 (((-.000595238095238 * z + .000793650793651) * z - .002777777777778) * z + 48 .083333333333333) / x
49 50
51 -def _incomplete_gamma(x, alpha):
52 """Compute an incomplete gamma ratio. 53 54 Comments from Z. Yang:: 55 56 Returns the incomplete gamma ratio I(x,alpha) where x is the upper 57 limit of the integration and alpha is the shape parameter. 58 returns (-1) if in error 59 ln_gamma_alpha = ln(Gamma(alpha)), is almost redundant. 60 (1) series expansion if alpha>x or x<=1 61 (2) continued fraction otherwise 62 RATNEST FORTRAN by 63 Bhattacharjee GP (1970) The incomplete gamma integral. Applied Statistics, 64 19: 285-287 (AS32) 65 66 """ 67 p = alpha 68 g = _ln_gamma_function(alpha) 69 accurate = 1e-8 70 overflow = 1e30 71 gin = 0 72 rn = 0 73 a = 0 74 b = 0 75 an = 0 76 dif = 0 77 term = 0 78 if x == 0: 79 return 0 80 if x < 0 or p <= 0: 81 return -1 82 factor = exp(p * log(x) - x - g) 83 if x > 1 and x >= p: 84 a = 1 - p 85 b = a + x + 1 86 term = 0 87 pn = [1, x, x + 1, x * b, None, None] 88 gin = pn[2] / pn[3] 89 else: 90 gin = 1 91 term = 1 92 rn = p 93 while term > accurate: 94 rn += 1 95 term *= x / rn 96 gin += term 97 gin *= factor / p 98 return gin 99 while True: 100 a += 1 101 b += 2 102 term += 1 103 an = a * term 104 for i in range(2): 105 pn[i + 4] = b * pn[i + 2] - an * pn[i] 106 if pn[5] != 0: 107 rn = pn[4] / pn[5] 108 dif = abs(gin - rn) 109 if dif > accurate: 110 gin = rn 111 elif dif <= accurate * rn: 112 break 113 for i in range(4): 114 pn[i] = pn[i + 2] 115 if abs(pn[4]) < overflow: 116 continue 117 for i in range(4): 118 pn[i] /= overflow 119 gin = 1 - factor * gin 120 return gin
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