feat: add math utils.

math/gaussian.go

@@ -0,0 +1,134 @@
+package math
+
+import (
+	"math"
+)
+
+// prop
+//mean: the mean (μ) of the distribution
+//variance: the variance (σ^2) of the distribution
+//standardDeviation: the standard deviation (σ) of the distribution
+
+// combination
+
+type Gaussian struct {
+	mean              float64
+	variance          float64
+	standardDeviation float64
+}
+
+func NewGaussian(mean, variance float64) *Gaussian {
+	if variance <= 0.0 {
+		panic("error")
+	}
+
+	return &Gaussian{
+		mean:              mean,
+		variance:          variance,
+		standardDeviation: math.Sqrt(float64(variance)),
+	}
+}
+
+// Erfc Complementary error function
+// From Numerical Recipes in C 2e p221
+func Erfc(x float64) float64 {
+	z := math.Abs(x)
+	t := 1 / (1 + z/2)
+	r := t * math.Exp(-z*z-1.26551223+t*(1.00002368+
+		t*(0.37409196+t*(0.09678418+t*(-0.18628806+
+			t*(0.27886807+t*(-1.13520398+t*(1.48851587+
+				t*(-0.82215223+t*0.17087277)))))))))
+	if x >= 0 {
+		return r
+	} else {
+		return 2 - r
+	}
+}
+
+// Ierfc Inverse complementary error function
+// From Numerical Recipes 3e p265
+func Ierfc(x float64) float64 {
+	if x >= 2 {
+		return -100
+	}
+	if x <= 0 {
+		return 100
+	}
+	var xx float64
+	if x < 1 {
+		xx = x
+	} else {
+		xx = 2 - x
+	}
+	t := math.Sqrt(-2 * math.Log(xx/2))
+	r := -0.70711 * ((2.30753+t*0.27061)/
+		(1+t*(0.99229+t*0.04481)) - t)
+
+	for j := 0; j < 2; j++ {
+		e := Erfc(r) - xx
+		r += e / (1.12837916709551257*math.Exp(-(r*r)) - r*e)
+	}
+
+	if x < 1 {
+		return r
+	} else {
+		return -r
+	}
+
+}
+
+// fromPrecisionMean Construct a new distribution from the precision and precisionmean
+func fromPrecisionMean(precision, precisionmean float64) *Gaussian {
+	return NewGaussian(precisionmean/precision, 1/precision)
+}
+
+/// PROB
+
+// Pdf pdf(x): the probability density function, which describes the probability
+// of a random variable taking on the value x
+func (g *Gaussian) Pdf(x float64) float64 {
+	m := g.standardDeviation * math.Sqrt(2*math.Pi)
+	e := math.Exp(-math.Pow(x-g.mean, 2) / (2 * g.variance))
+	return e / m
+}
+
+// Cdf cdf(x): the cumulative distribution function,
+// which describes the probability of a random
+// variable falling in the interval (−∞, x]
+func (g *Gaussian) Cdf(x float64) float64 {
+	return 0.5 * Erfc(-(x-g.mean)/(g.standardDeviation*math.Sqrt(2)))
+}
+
+// Ppf ppf(x): the percent point function, the inverse of cdf
+func (g *Gaussian) Ppf(x float64) float64 {
+	return g.mean - g.standardDeviation*math.Sqrt(2)*Ierfc(2*x)
+}
+
+// Add add(d): returns the result of adding this and the given distribution
+func (g *Gaussian) Add(d *Gaussian) *Gaussian {
+	return NewGaussian(g.mean+d.mean, g.variance+d.variance)
+}
+
+// Sub sub(d): returns the result of subtracting this and the given distribution
+func (g *Gaussian) Sub(d *Gaussian) *Gaussian {
+	return NewGaussian(g.mean-d.mean, g.variance+d.variance)
+}
+
+// Scale scale(c): returns the result of scaling this distribution by the given constant
+func (g *Gaussian) Scale(c float64) *Gaussian {
+	return NewGaussian(g.mean*c, g.variance*c*c)
+}
+
+// Mul mul(d): returns the product distribution of this and the given distribution. If a constant is passed in the distribution is scaled.
+func (g *Gaussian) Mul(d *Gaussian) *Gaussian {
+	precision := 1 / g.variance
+	dprecision := 1 / d.variance
+	return fromPrecisionMean(precision+dprecision, precision*g.mean+dprecision*d.mean)
+}
+
+// Div div(d): returns the quotient distribution of this and the given distribution. If a constant is passed in the distribution is scaled by 1/d.
+func (g *Gaussian) Div(d *Gaussian) *Gaussian {
+	precision := 1 / g.variance
+	dprecision := 1 / d.variance
+	return fromPrecisionMean(precision-dprecision, precision*g.mean-dprecision*d.mean)
+}