Module: Distribution::MathExtension::Erfc

Defined in:
lib/distribution/math_extension/erfc.rb

Overview

Error function from GSL-1.9, with epsilon information. Access it using Math.erfc_e

Constant Summary collapse

P = 
[2.97886562639399288862,
7.409740605964741794425,
6.1602098531096305440906,
5.019049726784267463450058,
1.275366644729965952479585264,
0.5641895835477550741253201704]
Q = 
[3.3690752069827527677,
9.608965327192787870698,
17.08144074746600431571095,
12.0489519278551290360340491,
9.396034016235054150430579648,
2.260528520767326969591866945,
1.0]

Class Method Summary collapse

Class Method Details

.erfc8(x) ⇒ Object 



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# File 'lib/distribution/math_extension/erfc.rb', line 33

def erfc8(x)
  erfc8_sum(x) * Math.exp(-x * x)
end

.erfc8_sum(x) ⇒ Object

Estimates erfc(x) valid for 8 < x < 100 erfc8_sum from GSL-1.9



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# File 'lib/distribution/math_extension/erfc.rb', line 25

def erfc8_sum(x)
  num = P[5]
  4.downto(0) { |i| num = x * num + P[i] }
  den = Q[6]
  5.downto(0) { |i| den = x * den + Q[i] }
  num / den
end

.evaluate(x, with_error = false) ⇒ Object

gsl_sf_erfc_e



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# File 'lib/distribution/math_extension/erfc.rb', line 38

def evaluate(x, with_error = false)
  ax = x.abs
  e = nil

  if ax <= 1.0
    t = 2 * ax - 1
    e = ChebyshevSeries.evaluate(:erfc_xlt1, t, with_error)
  elsif ax <= 5.0
    ex2 = Math.exp(-x * x)
    t   = (ax - 3).quo(2)
    e   = ChebyshevSeries.evaluate(:erfc_x15, t, with_error)
    if with_error
      e[0] *= ex2
      e[1] = ex2 * (e[1] + 2 * x.abs * Float::EPSILON)
    else
      e *= ex2
    end
  elsif ax < 10.0
    exterm = Math.exp(-x * x) / ax
    t      = (2 * ax - 15).quo(5)
    e = ChebyshevSeries.evaluate(:erfc_x510, t, with_error)
    if with_error
      e[0] *= exterm
      e[1] = exterm * (e[1] + 2 * x.abs * Float::EPSILON + Float::EPSILON)
    else
      e *= exterm
    end
  else
    e8 = erfc8(ax)
    e = with_error ? [e8, (x * x + 1) * Float::EPSILON * e8.abs] : e8
  end

  result = x < 0 ? 2 - (with_error ? e.first : e) : (with_error ? e.first : e)
  with_error ? [result, e.last + 2 * Float::EPSILON * result.abs] : result
end