special_functions.go

package math

import (
	"math"
)

// Inverse of the Error Function,
// function referenced from Apache commons-math Erf
func ErfInv(x float64) float64 {
	// beware that the logarithm argument must be
	// commputed as (1.0 - x) * (1.0 + x),
	// it must NOT be simplified as 1.0 - x * x as this
	// would induce rounding errors near the boundaries +/-1
	w := -math.Log((1.0 - x) * (1.0 + x))
	var p float64

	if w < 6.25 {
		w -= 3.125
		p = -3.6444120640178196996e-21
		p = -1.685059138182016589e-19 + p*w
		p = 1.2858480715256400167e-18 + p*w
		p = 1.115787767802518096e-17 + p*w
		p = -1.333171662854620906e-16 + p*w
		p = 2.0972767875968561637e-17 + p*w
		p = 6.6376381343583238325e-15 + p*w
		p = -4.0545662729752068639e-14 + p*w
		p = -8.1519341976054721522e-14 + p*w
		p = 2.6335093153082322977e-12 + p*w
		p = -1.2975133253453532498e-11 + p*w
		p = -5.4154120542946279317e-11 + p*w
		p = 1.051212273321532285e-09 + p*w
		p = -4.1126339803469836976e-09 + p*w
		p = -2.9070369957882005086e-08 + p*w
		p = 4.2347877827932403518e-07 + p*w
		p = -1.3654692000834678645e-06 + p*w
		p = -1.3882523362786468719e-05 + p*w
		p = 0.0001867342080340571352 + p*w
		p = -0.00074070253416626697512 + p*w
		p = -0.0060336708714301490533 + p*w
		p = 0.24015818242558961693 + p*w
		p = 1.6536545626831027356 + p*w
	} else if w < 16.0 {
		w = math.Sqrt(w) - 3.25
		p = 2.2137376921775787049e-09
		p = 9.0756561938885390979e-08 + p*w
		p = -2.7517406297064545428e-07 + p*w
		p = 1.8239629214389227755e-08 + p*w
		p = 1.5027403968909827627e-06 + p*w
		p = -4.013867526981545969e-06 + p*w
		p = 2.9234449089955446044e-06 + p*w
		p = 1.2475304481671778723e-05 + p*w
		p = -4.7318229009055733981e-05 + p*w
		p = 6.8284851459573175448e-05 + p*w
		p = 2.4031110387097893999e-05 + p*w
		p = -0.0003550375203628474796 + p*w
		p = 0.00095328937973738049703 + p*w
		p = -0.0016882755560235047313 + p*w
		p = 0.0024914420961078508066 + p*w
		p = -0.0037512085075692412107 + p*w
		p = 0.005370914553590063617 + p*w
		p = 1.0052589676941592334 + p*w
		p = 3.0838856104922207635 + p*w
	} else if !math.IsInf(w, 0) {
		w = math.Sqrt(w) - 5.0
		p = -2.7109920616438573243e-11
		p = -2.5556418169965252055e-10 + p*w
		p = 1.5076572693500548083e-09 + p*w
		p = -3.7894654401267369937e-09 + p*w
		p = 7.6157012080783393804e-09 + p*w
		p = -1.4960026627149240478e-08 + p*w
		p = 2.9147953450901080826e-08 + p*w
		p = -6.7711997758452339498e-08 + p*w
		p = 2.2900482228026654717e-07 + p*w
		p = -9.9298272942317002539e-07 + p*w
		p = 4.5260625972231537039e-06 + p*w
		p = -1.9681778105531670567e-05 + p*w
		p = 7.5995277030017761139e-05 + p*w
		p = -0.00021503011930044477347 + p*w
		p = -0.00013871931833623122026 + p*w
		p = 1.0103004648645343977 + p*w
		p = 4.8499064014085844221 + p*w

	} else {
		p = math.Inf(0)
	}

	return p * x
}

// Returns the inverse erfc.
func ErfcInv(x float64) float64 {
	return ErfInv(1 - x)
}