eta_index_lib/utils/calculate.go

package utils

import (
	"github.com/shopspring/decimal"
	"math"
)

// Series is a container for a series of data
type Series []Coordinate

// Coordinate holds the data in a series
type Coordinate struct {
	X, Y float64
}

// GetLinearResult 生成线性方程式
func GetLinearResult(s []Coordinate) (gradient, intercept float64) {
	if len(s) <= 1 {
		return
	}

	// Placeholder for the math to be done
	var sum [5]float64

	// Loop over data keeping index in place
	i := 0
	for ; i < len(s); i++ {
		sum[0] += s[i].X
		sum[1] += s[i].Y
		sum[2] += s[i].X * s[i].X
		sum[3] += s[i].X * s[i].Y
		sum[4] += s[i].Y * s[i].Y
	}

	// Find gradient and intercept
	f := float64(i)
	gradient = (f*sum[3] - sum[0]*sum[1]) / (f*sum[2] - sum[0]*sum[0])
	intercept = (sum[1] / f) - (gradient * sum[0] / f)

	//fmt.Println("gradient:", gradient, ";intercept:", intercept)
	// Create the new regression series
	//for j := 0; j < len(s); j++ {
	//	regressions = append(regressions, Coordinate{
	//		X: s[j].X,
	//		Y: s[j].X*gradient + intercept,
	//	})
	//}

	return
}

// ComputeCorrelation 通过一组数据获取相关系数R
// 计算步骤
// 1.分别计算两个序列的平均值Mx和My
// 2.分别计算两个序列的标准偏差SDx和SDy	=> √{1/(n-1)*SUM[(Xi-Mx)²]}
// 3.计算相关系数	=> SUM[(Xi-Mx)*(Yi-My)]/[(N-1)(SDx*SDy)]
func ComputeCorrelation(sList []Coordinate) (r float64) {
	var xBar, yBar float64
	lenSList := len(sList)
	// 必须两组数据及两组以上的数据才能计算
	if lenSList < 2 {
		return
	}
	decimalX := decimal.NewFromFloat(0)
	decimalY := decimal.NewFromFloat(0)

	// 计算两组数据X、Y的平均值
	for _, coordinate := range sList {
		decimalX = decimalX.Add(decimal.NewFromFloat(coordinate.X))
		decimalY = decimalY.Add(decimal.NewFromFloat(coordinate.Y))
	}
	xBar, _ = decimalX.Div(decimal.NewFromInt(int64(lenSList))).Round(4).Float64()
	yBar, _ = decimalY.Div(decimal.NewFromInt(int64(lenSList))).Round(4).Float64()
	//fmt.Println(xBar)
	//fmt.Println(yBar)

	varXDeci := decimal.NewFromFloat(0)
	varYDeci := decimal.NewFromFloat(0)
	ssrDeci := decimal.NewFromFloat(0)

	for _, coordinate := range sList {
		// 分别计算X、Y的实际数据与平均值的差值
		diffXXbarDeci := decimal.NewFromFloat(coordinate.X).Sub(decimal.NewFromFloat(xBar))
		diffYYbarDeci := decimal.NewFromFloat(coordinate.Y).Sub(decimal.NewFromFloat(yBar))
		ssrDeci = ssrDeci.Add(diffXXbarDeci.Mul(diffYYbarDeci))
		//fmt.Println("i：", i, ";diffXXbar:", diffXXbarDeci.String(), ";diffYYbar:", diffYYbarDeci.String(), ";ssr:", ssrDeci.String())
		varXDeci = varXDeci.Add(diffXXbarDeci.Mul(diffXXbarDeci))
		varYDeci = varYDeci.Add(diffYYbarDeci.Mul(diffYYbarDeci))
		//varY += diffYYbar ** 2
	}
	//当输入的两个数组完全相同时，计算相关系数会导致除以零的操作，从而产生 NaN（Not a Number）的结果。为了避免这种情况，可以在计算相关系数之前先进行一个判断，如果两个数组的标准差为零，则相关系数应为1
	if varXDeci.IsZero() && varYDeci.IsZero() {
		r = 1
		return
	}
	sqrtVal, _ := varXDeci.Mul(varYDeci).Round(4).Float64()
	//fmt.Println("sqrtVal:", sqrtVal)
	sst := math.Sqrt(sqrtVal) // 平方根
	//fmt.Println("sst:", sst)
	// 如果计算出来的平方根是0,那么就直接返回,因为0不能作为除数
	if sst == 0 {
		return
	}
	r, _ = ssrDeci.Div(decimal.NewFromFloat(sst)).Round(4).Float64()

	return
}

// CalculationDecisive 通过一组数据获取决定系数R2
func CalculationDecisive(sList []Coordinate) (r2 float64) {
	r := ComputeCorrelation(sList)
	r2, _ = decimal.NewFromFloat(r).Mul(decimal.NewFromFloat(r)).Round(4).Float64()

	return
}

// CalculateStandardDeviation 计算标准差
func CalculateStandardDeviation(data []float64) float64 {
	// 计算平均值
	mean := calculateMean(data)
	// 计算方差
	variance := calculateVariance(data, mean)
	return math.Sqrt(variance)
}

// 计算平均值
func calculateMean(data []float64) float64 {
	sum := 0.0
	for _, value := range data {
		sum += value
	}
	return sum / float64(len(data))
}

// 计算方差
func calculateVariance(data []float64, mean float64) float64 {
	sumSquaredDiff := 0.0
	for _, value := range data {
		diff := value - mean
		sumSquaredDiff += diff * diff
	}
	return sumSquaredDiff / float64(len(data))
}