Module: Distribution::MathExtension18

Included in:
Math
Defined in:
lib/distribution/math_extension.rb

Overview

Extension for Ruby18 Includes gamma and lgamma

Constant Summary collapse

LOG_2PI =

log(2PI)

Math.log(2 * Math::PI)
N = 
8
B0 = 
1.0
B1 = 
-1.0 / 2.0
B2 = 
1.0 / 6.0
B4 = 
-1.0 / 30.0
B6 = 
1.0 / 42.0
B8 = 
-1.0 / 30.0
B10 = 
5.0 / 66.0
B12 = 
-691.0 / 2730.0
B14 = 
7.0 / 6.0
B16 = 
-3617.0 / 510.0

Instance Method Summary collapse

Instance Method Details

#gamma(x) ⇒ Object

Gamma function. From statistics2



55
56
57
58
59
60
 
# File 'lib/distribution/math_extension.rb', line 55

def gamma(x)
  if (x < 0.0)
    return Math::PI / (Math.sin(Math.PI * x) * Math.exp(loggamma(1 - x))) #/
  end
  Math.exp(loggamma(x))
end

#loggamma(x) ⇒ Object

From statistics2



34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
 
# File 'lib/distribution/math_extension.rb', line 34

def loggamma(x)
  v = 1.0
  while (x < N)
    v *= x
    x += 1.0
  end
  w = 1.0 / (x * x)
  ret = B16 / (16 * 15)
  ret = ret * w + B14 / (14 * 13)
  ret = ret * w + B12 / (12 * 11)
  ret = ret * w + B10 / (10 *  9)
  ret = ret * w + B8  / ( 8 *  7)
  ret = ret * w + B6  / ( 6 *  5)
  ret = ret * w + B4  / ( 4 *  3)
  ret = ret * w + B2  / ( 2 *  1)
  ret = ret / x + 0.5 * LOG_2PI - Math.log(v) - x + (x - 0.5) * Math.log(x)
  ret
end