예제 #1
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// Inverse of complementary error function. Returns x such that erfc(x) = p for argument p.
func InvErfc(p float64) float64 {
	// From page 265 of numerical recipes
	if p >= 2.0 {
		return -100
	}
	if p <= 0.0 {
		return 100
	}

	var pp float64
	if p < 1.0 {
		pp = p
	} else {
		pp = 2 - p
	}

	t := math.Sqrt(-2 * math.Log(pp/2.0)) // Initial guess
	x := -0.70711 * ((2.30753+t*0.27061)/(1.0+t*(0.99229+t*0.04481)) - t)

	for j := 0; j < 2; j++ {
		err := math.Erfc(x) - pp
		x += err / (1.12837916709551257*math.Exp(-(x*x)) - x*err) // Halley
	}

	if p < 1.0 {
		return x
	}
	return -x
}
예제 #2
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func (n NormalDist) cdfEach(xs []float64) []float64 {
	res := make([]float64, len(xs))
	a := 1 / (n.Sigma * math.Sqrt2)
	for i, x := range xs {
		res[i] = math.Erfc(-(x-n.Mu)*a) / 2
	}
	return res
}
예제 #3
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// Erfc returns the complementary error function of x (from math.Erfc).
func Erfc(x float64) float64 {
	return math.Erfc(x)
}
예제 #4
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// Erfc returns the complementary error function of x.
//
// Special cases are:
//	Erfc(+Inf) = 0
//	Erfc(-Inf) = 2
//	Erfc(NaN) = NaN
func Erfc(x float32) float32 {
	return float32(math.Erfc(float64(x)))
}
예제 #5
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func (n NormalDist) InvCDF(p float64) (x float64) {
	// This is based on Peter John Acklam's inverse normal CDF
	// algorithm: http://home.online.no/~pjacklam/notes/invnorm/
	const (
		a1 = -3.969683028665376e+01
		a2 = 2.209460984245205e+02
		a3 = -2.759285104469687e+02
		a4 = 1.383577518672690e+02
		a5 = -3.066479806614716e+01
		a6 = 2.506628277459239e+00

		b1 = -5.447609879822406e+01
		b2 = 1.615858368580409e+02
		b3 = -1.556989798598866e+02
		b4 = 6.680131188771972e+01
		b5 = -1.328068155288572e+01

		c1 = -7.784894002430293e-03
		c2 = -3.223964580411365e-01
		c3 = -2.400758277161838e+00
		c4 = -2.549732539343734e+00
		c5 = 4.374664141464968e+00
		c6 = 2.938163982698783e+00

		d1 = 7.784695709041462e-03
		d2 = 3.224671290700398e-01
		d3 = 2.445134137142996e+00
		d4 = 3.754408661907416e+00

		plow  = 0.02425
		phigh = 1 - plow
	)

	if p < 0 || p > 1 {
		return nan
	} else if p == 0 {
		return -inf
	} else if p == 1 {
		return inf
	}

	if p < plow {
		// Rational approximation for lower region.
		q := math.Sqrt(-2 * math.Log(p))
		x = (((((c1*q+c2)*q+c3)*q+c4)*q+c5)*q + c6) /
			((((d1*q+d2)*q+d3)*q+d4)*q + 1)
	} else if phigh < p {
		// Rational approximation for upper region.
		q := math.Sqrt(-2 * math.Log(1-p))
		x = -(((((c1*q+c2)*q+c3)*q+c4)*q+c5)*q + c6) /
			((((d1*q+d2)*q+d3)*q+d4)*q + 1)
	} else {
		// Rational approximation for central region.
		q := p - 0.5
		r := q * q
		x = (((((a1*r+a2)*r+a3)*r+a4)*r+a5)*r + a6) * q /
			(((((b1*r+b2)*r+b3)*r+b4)*r+b5)*r + 1)
	}

	// Refine approximation.
	e := 0.5*math.Erfc(-x/math.Sqrt2) - p
	u := e * math.Sqrt(2*math.Pi) * math.Exp(x*x/2)
	x = x - u/(1+x*u/2)

	// Adjust from standard normal.
	return x*n.Sigma + n.Mu
}
예제 #6
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func (n NormalDist) CDF(x float64) float64 {
	return math.Erfc(-(x-n.Mu)/(n.Sigma*math.Sqrt2)) / 2
}