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)
+}

math/gaussian_test.go

@@ -0,0 +1,47 @@
+package math
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestGaussian(t *testing.T) {
+	g := NewGaussian(3.0, 1)
+
+	fmt.Printf("g: %#v\n", g)
+	fmt.Printf("pdf: %f\n", g.Pdf(5))
+	fmt.Printf("cdf: %f\n", g.Cdf(2))
+	fmt.Printf("ppf: %f\n", g.Ppf(5))
+
+	d := NewGaussian(0, 1)
+	fmt.Printf("ppf: %f, %f\n", d.Pdf(-2), 0.053991)
+	fmt.Printf("ppf: %f, %f\n", d.Pdf(-1), 0.241971)
+	fmt.Printf("ppf: %f, %f\n", d.Pdf(0), 0.398942)
+	fmt.Printf("ppf: %f, %f\n", d.Pdf(1), 0.241971)
+	fmt.Printf("ppf: %f, %f\n", d.Pdf(2), 0.053991)
+
+	fmt.Printf("cdf: %f, %f\n", d.Cdf(-1.28155), 0.1)
+	fmt.Printf("cdf: %f, %f\n", d.Cdf(-0.67499), 0.25)
+	fmt.Printf("cdf: %f, %f\n", d.Cdf(0), 0.5)
+	fmt.Printf("cdf: %f, %f\n", d.Cdf(0.67499), 0.75)
+	fmt.Printf("cdf: %f, %f\n", d.Cdf(1.28155), 0.9)
+
+	fmt.Printf("ppf: %f, %f\n", d.Ppf(0.1), -1.28155)
+	fmt.Printf("ppf: %f, %f\n", d.Ppf(0.25), -0.67499)
+	fmt.Printf("ppf: %f, %f\n", d.Ppf(0.5), 0.0)
+	fmt.Printf("ppf: %f, %f\n", d.Ppf(0.75), 0.67449)
+	fmt.Printf("ppf: %f, %f\n", d.Ppf(0.9), 1.28155)
+
+	d = d.Mul(NewGaussian(0, 1))
+	fmt.Printf("Mul: %#v\n", d)
+	fmt.Printf("%#v\n%#v", NewGaussian(1, 1).Scale(2), NewGaussian(2, 4))
+
+	d = NewGaussian(1, 1).Div(NewGaussian(1, 2))
+	fmt.Printf("div\n")
+	fmt.Printf("%#v\n%#v\n", d, NewGaussian(1, 2))
+	fmt.Printf("%#v\n%#v\n", NewGaussian(1, 1).Scale(1/(1.0/2.0)), NewGaussian(2, 4))
+
+	fmt.Printf("ADD:\n%#v\n%#v\n", NewGaussian(1, 1).Add(NewGaussian(1, 2)), NewGaussian(2, 3))
+	fmt.Printf("SUB:\n%#v\n%#v\n", NewGaussian(1, 1).Sub(NewGaussian(1, 2)), NewGaussian(0, 3))
+	fmt.Printf("SCALE:\n%#v\n%#v\n", NewGaussian(1, 1).Scale(2), NewGaussian(2, 4))
+}

math/math.go

@@ -0,0 +1,44 @@
+package math
+
+import (
+	"math"
+)
+
+// Sign 符号函数（Sign function，简称sgn）是一个逻辑函数，用以判断实数的正负号。为避免和英文读音相似的正弦函数（sine）混淆，它亦称为Signum function。
+func Sign[T int | int8 | int16 | int32 | int64 | float32 | float64](x T) T {
+	switch {
+	case x < 0: // x < 0 : -1
+		return -1
+	case x > 0: // x > 0 : +1
+		return +1
+	default: // x == 0 : 0
+		return 0
+	}
+}
+
+// Mean 计算给定数据的平均值
+func Mean(num []float64) float64 {
+	var count = len(num)
+	var sum float64 = 0
+	for i := 0; i < count; i++ {
+		sum += num[i]
+	}
+	return sum / float64(count)
+}
+
+// Variance 使用平均值计算给定数据的方差
+func Variance(mean float64, num []float64) float64 {
+	var count = len(num)
+	var variance float64 = 0
+	for i := 0; i < count; i++ {
+		variance += math.Pow(num[i]-mean, 2)
+	}
+	return variance / float64(count)
+}
+
+// StandardDeviation 使用方差计算给定数据的标准偏差
+func StandardDeviation(num []float64) float64 {
+	var mean = Mean(num)
+	var variance = Variance(mean, num)
+	return math.Sqrt(variance)
+}

math/math_test.go

@@ -0,0 +1,30 @@
+package math
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestSign(t *testing.T) {
+	assert.True(t, Sign(2) == 1)
+	assert.True(t, Sign(-2) == -1)
+	assert.True(t, Sign(0) == 0)
+
+	assert.True(t, Sign(int64(2)) == 1)
+	assert.True(t, Sign(int64(-2)) == -1)
+	assert.True(t, Sign(int64(0)) == 0)
+
+	assert.True(t, Sign(float32(2)) == 1)
+	assert.True(t, Sign(float32(-2)) == -1)
+	assert.True(t, Sign(float32(0)) == 0)
+
+	assert.True(t, Sign(float64(2)) == 1)
+	assert.True(t, Sign(float64(-2)) == -1)
+	assert.True(t, Sign(float64(0)) == 0)
+}
+
+func TestStandardDeviation(t *testing.T) {
+	assert.Equal(t, StandardDeviation([]float64{3, 5, 9, 1, 8, 6, 58, 9, 4, 10}), 15.8117045254457)
+	assert.Equal(t, StandardDeviation([]float64{1, 3, 5, 7, 9, 11, 2, 4, 6, 8}), 3.0397368307141326)
+}